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A086229 Determinant of n X n matrix M(i,j) = binomial(2i-1,j), (i,j) ranging from 1 to n. 1
1, 1, 3, 20, 280, 8064, 473088, 56229888, 13495173120, 6525665935360, 6348167821918208, 12410090985684467712, 48713743815806763925504, 383714412826047125074739200, 6062249191894029093752222515200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = 2^(n*(n-3)/2)*binomial(2*n, n).

a(n) = 2^C(n,2)*Hypergeometric2F1((1-n)/2,-n/2;1;1).

MATHEMATICA

f[n_] := 2^(n (n - 3)/2) Binomial[2 n, n]; (* Or *)

f[n_] := 2^(n (n - 1)/2) Hypergeometric2F1[(1 - n)/2, -n/2, 1, 1]; Array[f, 15, 0]  (* Robert G. Wilson v *)

PROG

(PARI) a(n) = matdet(matrix(n, n, i, j, binomial(2*i-1, j))); \\ Michel Marcus, Dec 12 2014

CROSSREFS

Sequence in context: A166232 A136551 A266812 * A130531 A240777 A163138

Adjacent sequences:  A086226 A086227 A086228 * A086230 A086231 A086232

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Aug 28 2003

STATUS

approved

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Last modified March 22 22:05 EDT 2017. Contains 283901 sequences.