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A295871
a(n) = numerator(hypergeom([-n, 1/2], [1], 1)*hypergeom([-floor(n/2), (-1)^n/2], [1], 1)).
0
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
0,3
FORMULA
a(n) = numerator(4^(-n-floor(n/2))*binomial(2*n,n)*n!/floor(n/2)!^2).
MAPLE
seq(numer(4^(-n-floor(n/2))*binomial(2*n, n)*n!/iquo(n, 2)!^2), n=0..23);
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}]
PROG
(PARI) a(n) = numerator(4^(-n-floor(n/2))*binomial(2*n, n)*n!/floor(n/2)!^2); \\ Michel Marcus, Feb 15 2018
CROSSREFS
Cf. A295864.
Sequence in context: A360579 A251598 A338725 * A293997 A328866 A247304
KEYWORD
nonn,frac
AUTHOR
Peter Luschny, Feb 14 2018
STATUS
approved