A306280 a(n) = Sum_{k=0..n} binomial(n,k)*binomial(n^2+k,k).

1, 3, 26, 416, 9708, 297662, 11306572, 512307336, 26968496504, 1617489748394, 108885682104744, 8129721925098468, 666736347200187804, 59582961423951290184, 5762936296492591067968, 599807329803134064385488, 66843498592187788579795440

Offset: 0

Author

Seiichi Manyama, Feb 02 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..337

Crossrefs

Cf. A001850, A114496, A135860, A156886, A156887.

Programs

Mathematica

a[n_] := Sum[Binomial[n,k] * Binomial[n^2+k,k], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Feb 03 2019 *)

PARI

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

Formula

From Vaclav Kotesovec, Feb 08 2019: (Start)

a(n) ~ exp(1) * A135860(n).

a(n) ~ exp(n + 3/2) * n^(n - 1/2) / sqrt(2*Pi). (End)