A370704 a(n) = Sum_{k=0..n} k!*binomial(n, k)*Pochhammer(n, k). Row sums of A370707.

1, 2, 17, 442, 23297, 2029226, 262403857, 47086207442, 11184381577217, 3395509635512242, 1282288601819184401, 589443236677619916362, 324023682525763528809217, 209882061169585594259778842, 158200294157346855067204600337, 137282439597406466709932610293026

Offset: 0

Author

Peter Luschny, Feb 28 2024

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A370707.

Programs

Maple

a := n -> local k, j; add((-1)^k * mul((j - n)*(j + n), j = 0..k-1), k = 0..n):
seq(a(n), n = 0..15);

Mathematica

A370704[n_] := Sum[k!*Binomial[n, k]*Pochhammer[n, k], {k, 0, n}];
Array[A370704, 20, 0] (* Paolo Xausa, Mar 07 2024 *)

Formula

a(n) = Sum_{k=0..n} (-1)^k*Product_{j=0..k-1} (j - n)*(j + n).

a(n) ~ sqrt(Pi) * 4^n * n^(2*n + 1/2) / exp(2*n). - Vaclav Kotesovec, Mar 12 2024