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%I #12 Feb 15 2018 05:07:06
%S 1,1,3,15,105,945,1155,15015,225225,3828825,2909907,61108047,
%T 156165009,3904125225,2151252675,62386327575,1933976154825,
%U 63821213109225,27577067392875,1020351493536375,1591748329916745,65261681526586545,23192167815233235,1043647551685495575
%N a(n) = numerator(hypergeom([-n, 1/2], [1], 1)*hypergeom([-floor(n/2), (-1)^n/2], [1], 1)).
%F a(n) = numerator(4^(-n-floor(n/2))*binomial(2*n,n)*n!/floor(n/2)!^2).
%p seq(numer(4^(-n-floor(n/2))*binomial(2*n,n)*n!/iquo(n,2)!^2), n=0..23);
%t a[n_] := Numerator[Hypergeometric2F1[-n, 1/2, 1, 1] Hypergeometric2F1[-Floor[n/2], (-1)^n/2, 1, 1]]; Table[a[n], {n, 0, 22}]
%o (PARI) a(n) = numerator(4^(-n-floor(n/2))*binomial(2*n,n)*n!/floor(n/2)!^2); \\ _Michel Marcus_, Feb 15 2018
%Y Cf. A295864.
%K nonn,frac
%O 0,3
%A _Peter Luschny_, Feb 14 2018
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