A350719 a(n) = Sum_{k=0..n} k! * 2^k * k^n * Stirling1(n,k).

1, 2, 30, 1108, 76372, 8463328, 1375868768, 308440047648, 91189383264864, 34376022491122368, 16093445542120281792, 9160424435706947112576, 6230035512106223752576896, 4989402076922846372194268160, 4647526704475074504983564884992

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..221

Formula

E.g.f.: Sum_{k>=0} (2 * log(1 + k*x))^k.

Mathematica

a[0] = 1; a[n_] := Sum[k! * 2^k * k^n * StirlingS1[n, k], {k, 1, n}]; Array[a, 15, 0] (* Amiram Eldar, Feb 03 2022 *)

Prog

(PARI) a(n) = sum(k=0, n, k!*2^k*k^n*stirling(n, k, 1));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (2*log(1+k*x))^k)))

Crossrefs

Cf. A320083, A350720.

Cf. A088501, A195005, A350721.

Sequence in context: A273661 A322624 A338044 * A140174 A246741 A089016

Adjacent sequences: A350716 A350717 A350718 * A350720 A350721 A350722

Keyword

nonn

Author

Seiichi Manyama, Feb 03 2022

Status

approved