A320502 a(n) = Sum_{k=0..n} (k!)^2 * abs(Stirling1(n,k)).

1, 1, 5, 50, 842, 21644, 792676, 39297600, 2536525008, 206794669104, 20785423425264, 2525457805492896, 364910211591903072, 61847041340997089280, 12151693924459271926272, 2739901558132307387349504, 702704348810821821056454144, 203409730893592265642619623424

Offset: 0

Author

Vaclav Kotesovec, Oct 13 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..253

Crossrefs

Cf. A000670, A007840, A064618, A192554.

Programs

Magma

[(&+[Abs(StirlingFirst(n,k))*(Factorial(k))^2: k in [0..n]]): n in [0..20]]; // G. C. Greubel, Oct 14 2018

Mathematica

Table[Sum[Abs[StirlingS1[n, k]]*k!^2, {k, 0, n}], {n, 0, 20}]

PARI

a(n) = sum(k=0, n, k!^2*abs(stirling(n, k, 1))); \\ Michel Marcus, Oct 14 2018

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, k!*(-log(1-x))^k))) \\ Seiichi Manyama, Apr 22 2022

Formula

a(n) ~ exp(1/2) * (n!)^2.

E.g.f.: Sum_{k>=0} k! * (-log(1-x))^k. - Seiichi Manyama, Apr 22 2022