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A192565 a(n) = sum(abs(stirling1(n+1,k+1))*stirling2(n,k)*k!^2,k=0..n). 0
1, 1, 7, 119, 3766, 191074, 14190940, 1451180016, 195500153984, 33556323694176, 7148802130010784, 1850863101948856368, 572367322411341168960, 208372437783910651168800, 88211625475147231105812096, 42967145403522500557662391104 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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 = 0.5694875599509546909505843910919946016728003129830561427442509356... - Vaclav Kotesovec, Jul 05 2021
MATHEMATICA
Table[Sum[Abs[StirlingS1[n+1, k+1]]StirlingS2[n, k]k!^2, {k, 0, n}], {n, 0, 100}]
PROG
(Maxima) makelist(sum(abs(stirling1(n+1, k+1))*stirling2(n, k)*k!^2, k, 0, n), n, 0, 24);
CROSSREFS
Sequence in context: A304917 A113667 A357351 * A171209 A296731 A092612
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Jul 04 2011
STATUS
approved

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Last modified March 28 13:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)