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mathematical analysis > combinatorics > binomial coefficient > central binomial coefficient

algebra > combinatorics > binomial coefficient > central binomial coefficient

Preferred term

central binomial coefficient

In mathematics the nth central binomial coefficient is the particular binomial coefficient
${\\displaystyle {2n \\choose n}={\ rac {(2n)!}{(n!)^{2}}}=\\prod \\limits _{k=1}^{n}{\ rac {n+k}{k}}{\ ext{ for all }}n\\geq 0.}$
They are called central since they show up exactly in the middle of the even-numbered rows in Pascal's triangle. The first few central binomial coefficients starting at n = 0 are:
1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, ...; (sequence A000984 in the OEIS)

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Central_binomial_coefficient)

binomial coefficient

coefficient binomial central

French

URI

http://data.loterre.fr/ark:/67375/PSR-TF44DDMB-4

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