A192567 a(n) = sum(abs(stirling1(n+1,k+1))*stirling2(n+1,k+1)*k!^2,k=0..n).

1, 2, 15, 263, 8450, 432514, 32308948, 3317537208, 448304831744, 77131843774416, 16463316260454624, 4269057157148962320, 1321883141629335120576, 481761671427370573812000, 204137795884403682574690176, 99514256070766872294586292544

Offset

0,2

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 = 1.333855551736054319768931910172827342915539397625400733803588773... - Vaclav Kotesovec, Jul 05 2021

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A102555 A264907 A195737 * A354980 A143886 A174482

Adjacent sequences: A192564 A192565 A192566 * A192568 A192569 A192570

Keyword

nonn

Author

Emanuele Munarini, Jul 04 2011

Status

approved