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# Double factorial

In mathematics, the double factorial or semifactorial of a number (denoted by) is the product of all the integers from 1 up to that have the same parity (odd or even) as. [1]

## American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

## Bijective proof

In combinatorics, bijective proof is a proof technique that finds a bijective function f: A → B between two finite sets A and B, or a size-preserving bijective function between two combinatorial classes, thus proving that they have the same number of elements, |A|.

## Binary tree

In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the and the.

## Binomial coefficient

In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.

## Catalan number

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects.

## Combinatorial class

In mathematics, a combinatorial class is a countable set of mathematical objects, together with a size function mapping each object to a non-negative integer, such that there are finitely many objects of each size.

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## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

## Empty product

In mathematics, an empty product, or nullary product, is the result of multiplying no factors.

## Enumerative combinatorics

Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed.

## Euler tour technique

The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees.

## Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.

## Falling and rising factorials

In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as The rising factorial (sometimes called the Pochhammer function, Pochhammer polynomial, ascending factorial, (A reprint of the 1950 edition by Chelsea Publishing Co.) rising sequential product, or upper factorial) is defined as The value of each is taken to be 1 (an empty product) when n.

## Gamma function

In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.

## Generating function

In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.

## Heap (data structure)

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. The node at the "top" of the heap (with no parents) is called the root node.

## Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

## Hyperoctahedral group

In mathematics, a hyperoctahedral group is an important type of group that can be realized as the group of symmetries of a hypercube or of a cross-polytope.

## Hypersphere

In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.

## Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

## Journal of Algebraic Combinatorics

Journal of Algebraic Combinatorics is a peer-reviewed scientific journal covering algebraic combinatorics.

## Journal of Computational Biology

The Journal of Computational Biology is a monthly peer-reviewed scientific journal covering computational biology and bioinformatics.

## List of integrals of trigonometric functions

The following is a list of integrals (antiderivative functions) of trigonometric functions.

## Matching (graph theory)

In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Mathematics Magazine

Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.

Mixed radix numeral systems are non-standard positional numeral systems in which the numerical base varies from position to position.

## Multiset

In mathematics, a multiset (aka bag or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements.

## N-sphere

In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.

## Numeral system

A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

## Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.

## Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

## Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.

## Richard Brauer

Richard Dagobert Brauer (February 10, 1901 &ndash; April 17, 1977) was a leading German and American mathematician.

## Stirling numbers of the first kind

In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations.

## Stirling permutation

In combinatorial mathematics, a Stirling permutation of order k is a permutation of the multiset 1, 1, 2, 2,..., k, k (with two copies of each value from 1 to k) with the additional property that, for each value i appearing in the permutation, the values between the two copies of i are larger than i. For instance, the 15 Stirling permutations of order three are The number of Stirling permutations of order k is given by the double factorial (2k &minus; 1)!!.

## Student's t-distribution

In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

## Telephone number (mathematics)

In mathematics, the telephone numbers or the involution numbers are a sequence of integers that count the ways telephone lines can be connected to each other, where each line can be connected to at most one other line.

## Unrooted binary tree

In mathematics and computer science, an unrooted binary tree is an unrooted tree in which each vertex has either one or three neighbors.

## Volume of an n-ball

In geometry, a ball is a region in space comprising all points within a fixed distance from a given point; that is, it is the region enclosed by a sphere or hypersphere.

## Wallis product

In mathematics, Wallis' product for pi, written down in 1655 by John Wallis, states that \prod_^ \left(\frac \cdot \frac\right).

## William Sealy Gosset

William Sealy Gosset (13 June 1876 – 16 October 1937) was an English statistician.

## Zeros and poles

In mathematics, a zero of a function is a value such that.

## References

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