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%I #24 Sep 08 2022 08:45:11
%S 1,1,3,20,280,8064,473088,56229888,13495173120,6525665935360,
%T 6348167821918208,12410090985684467712,48713743815806763925504,
%U 383714412826047125074739200,6062249191894029093752222515200
%N Determinant of n X n matrix M(i,j) = binomial(2i-1,j), (i,j) ranging from 1 to n.
%H G. C. Greubel, <a href="/A086229/b086229.txt">Table of n, a(n) for n = 0..80</a>
%F a(n) = 2^(n*(n-3)/2)*binomial(2*n, n).
%F a(n) = 2^C(n,2)*Hypergeometric2F1((1-n)/2,-n/2;1;1).
%t f[n_] := 2^(n (n - 3)/2) Binomial[2 n, n]; (* Or *)
%t f[n_] := 2^(n (n - 1)/2) Hypergeometric2F1[(1 - n)/2, -n/2, 1, 1]; Array[f, 15, 0] (* _Robert G. Wilson v_ *)
%o (PARI) a(n) = matdet(matrix(n, n, i, j, binomial(2*i-1, j))); \\ _Michel Marcus_, Dec 12 2014
%o (PARI) for(n=0, 30, print1(2^(n*(n-3)/2)*binomial(2*n, n), ", ")) \\ _G. C. Greubel_, Jan 25 2018
%o (Magma) [2^(n*(n-3)/2)*Binomial(2*n, n): n in [0..30]]; // _G. C. Greubel_, Jan 25 2018
%K nonn
%O 0,3
%A _Benoit Cloitre_, Aug 28 2003
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