A337420 a(n) = Sum_{k=0..n} (-n)^(n-k) * binomial(2*k,k) * binomial(2*n,2*k).

1, 1, -14, -7, 1222, -14873, 26196, 3522955, -110841786, 2088947819, -15869398244, -823790768205, 55262757020956, -2199333670723343, 65894251730104552, -1235877788883794355, -18904175519674543546, 3743957841955101437667, -268850524243738610546292, 14826380281246309472525851

Offset: 0

Author

Seiichi Manyama, Aug 27 2020

Keywords

• sign

Crossrefs

Main diagonal of A337419.

Cf. A337388.

Programs

Mathematica

a[n_] := Sum[If[n == 0, Boole[n == k], (-n)^(n - k)] * Binomial[2*k, k] * Binomial[2*n, 2*k], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Aug 27 2020 *)

PARI

{a(n) = sum(k=0, n, (-n)^(n-k)*binomial(2*k, k)*binomial(2*n, 2*k))}