A295871 a(n) = numerator(hypergeom([-n, 1/2], [1], 1)*hypergeom([-floor(n/2), (-1)^n/2], [1], 1)).
1, 1, 3, 15, 105, 945, 1155, 15015, 225225, 3828825, 2909907, 61108047, 156165009, 3904125225, 2151252675, 62386327575, 1933976154825, 63821213109225, 27577067392875, 1020351493536375, 1591748329916745, 65261681526586545, 23192167815233235, 1043647551685495575
Offset: 0
Crossrefs
Cf. A295864.
Programs
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Maple
seq(numer(4^(-n-floor(n/2))*binomial(2*n,n)*n!/iquo(n,2)!^2), n=0..23);
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Mathematica
a[n_] := Numerator[Hypergeometric2F1[-n, 1/2, 1, 1] Hypergeometric2F1[-Floor[n/2], (-1)^n/2, 1, 1]]; Table[a[n], {n, 0, 22}] -
PARI
a(n) = numerator(4^(-n-floor(n/2))*binomial(2*n,n)*n!/floor(n/2)!^2); \\ Michel Marcus, Feb 15 2018
Formula
a(n) = numerator(4^(-n-floor(n/2))*binomial(2*n,n)*n!/floor(n/2)!^2).