A192564 a(n) = sum(abs(stirling1(n,k))*stirling2(n,k)*k!^2,k=0..n).

1, 1, 5, 74, 2186, 106524, 7703896, 773034912, 102673179360, 17429291711280, 3680338415133024, 945958227345434016, 290761516548473591232, 105309706114422166775040, 44384982810939832477305600, 21536846291826596564956445184

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 = 0.27034346270211507329954765593360596752557904498770241464597402478625037569... - Vaclav Kotesovec, Jul 05 2021

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A370463 A126740 A251666 * A080473 A266570 A355121

Adjacent sequences: A192561 A192562 A192563 * A192565 A192566 A192567

Keyword

nonn

Author

Emanuele Munarini, Jul 04 2011

Status

approved