A192566 a(n) = Sum_{k=0..n} abs(stirling1(n,k))*stirling2(n+1,k+1)*k!^2.

1, 1, 7, 122, 3926, 201444, 15081256, 1551423600, 209964727584, 36170279518320, 7728442094221344, 2005825817037374496, 621563279659462241856, 226678766174046141016320, 96106307573596013377908480, 46874174201481263768233403904

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(n) ~ c * LambertW(-1, -r*exp(-r))^n * n!^2 / (sqrt(n) * LambertW(-exp(-1/r)/r)^n), where r = 0.673313285145753168... is the root of the equation (1 + 1/(r*LambertW(-exp(-1/r)/r))) * (r + LambertW(-1, -r*exp(-r))) = 1 and c = 0.63319930751748217157127596837987799731063242340102342707708047131... - Vaclav Kotesovec, Jul 05 2021

Mathematica

Table[Sum[Abs[StirlingS1[n, k]]StirlingS2[n+1, k+1]k!^2, {k, 0, n}], {n, 0, 100}]

Prog

(Maxima) makelist(sum(abs(stirling1(n, k))*stirling2(n+1, k+1)*k!^2, k, 0, n), n, 0, 24);

Crossrefs

Sequence in context: A012103 A012086 A074487 * A322090 A360337 A304420

Adjacent sequences: A192563 A192564 A192565 * A192567 A192568 A192569

Keyword

nonn

Author

Emanuele Munarini, Jul 04 2011

Status

approved