A086229 Determinant of n X n matrix M(i,j) = binomial(2i-1,j), (i,j) ranging from 1 to n.

1, 1, 3, 20, 280, 8064, 473088, 56229888, 13495173120, 6525665935360, 6348167821918208, 12410090985684467712, 48713743815806763925504, 383714412826047125074739200, 6062249191894029093752222515200

Offset: 0

Author

Benoit Cloitre, Aug 28 2003

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..80

Programs

Magma

[2^(n*(n-3)/2)*Binomial(2*n, n): n in [0..30]]; // G. C. Greubel, Jan 25 2018

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 *)

PARI

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

PARI

for(n=0, 30, print1(2^(n*(n-3)/2)*binomial(2*n, n), ", ")) \\ G. C. Greubel, Jan 25 2018

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).