A358695 a(n) = numerator( Sum_{k=0..n} (-1)^k * binomial(1/2, k)^2 * binomial(n, k) ).

1, 3, 33, 75, 1305, -8253, -340711, -2173509, -758532375, -3823240245, -73518428511, -342444310533, -24952606638687, -111735599023125, -1975318542049815, -8639356601706213, -9590905885722547959, -41296955508208952901, -707029904720030040775, -3010762771187568788685

Offset: 0

Author

Peter Luschny, Dec 08 2022

Keywords

• sign
• frac

Crossrefs

Cf. A056982 (denominators), A260832, A358113.

Programs

Maple

a := n -> numer(simplify(hypergeom([-1/2, -1/2, -n], [1, 1], 1))):
seq(a(n), n = 0..19);

Mathematica

a[n_] := Numerator[HypergeometricPFQ[{-1/2, -1/2, -n}, {1, 1}, 1]]; Array[a, 20, 0] (* Amiram Eldar, Dec 08 2022 *)

Formula

a(n) = numerator(hypergeometric([-1/2, -1/2, -n], [1, 1], 1)).

a(n) = numerator(A358113(n) / 16^n). - Andrey Zabolotskiy, Dec 08 2022