A350720 a(n) = Sum_{k=0..n} k! * 3^k * k^n * Stirling1(n,k).

1, 3, 69, 3948, 422082, 72567522, 18304992558, 6367730357160, 2921446409138136, 1709074810258369776, 1241694104839498851552, 1096850187800368469477424, 1157691464039682741551221152, 1438880771284303822650674399664

Offset: 0

Author

Seiichi Manyama, Feb 03 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..213

Crossrefs

Cf. A320083, A350719.

Cf. A195263, A335531, A350721.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[k! * 3^k * k^n * StirlingS1[n, k], {k, 1, n}]; Array[a, 14, 0] (* Amiram Eldar, Feb 03 2022 *)

PARI

a(n) = sum(k=0, n, k!*3^k*k^n*stirling(n, k, 1));

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*log(1+k*x))^k)))

Formula

E.g.f.: Sum_{k>=0} (3 * log(1 + k*x))^k.