A290840 a(n) = n! * [x^n] exp(n*x)/(1 + LambertW(-x)).

1, 2, 12, 117, 1584, 27525, 585108, 14726411, 428551616, 14161828185, 523952280900, 21456869976135, 963553844335536, 47078974421716757, 2486272976536821332, 141118622400977894475, 8566597074999702384384, 553816179165426157329201, 37985975117322654130568964

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..365

N. J. A. Sloane, Transforms

Martin Svatoš, Peter Jung, Jan Tóth, Yuyi Wang, and Ondřej Kuželka, On Discovering Interesting Combinatorial Integer Sequences, arXiv:2302.04606 [cs.LO], 2023, p. 17.

Formula

a(n) = A290824(n,n).

a(n) ~ exp(1/2 + n*exp(-1)) * n^n / sqrt(exp(1)-1). - Vaclav Kotesovec, Oct 06 2017

a(n) = Sum_{k=0..n} binomial(n,k)*n^(n-k)*k^k. - Fabian Pereyra, Jul 16 2024

E.g.f.: 1/((1+LambertW(-x))*(1+LambertW(LambertW(-x)))). - Fabian Pereyra, Jul 19 2024

Mathematica

Table[n! * SeriesCoefficient[Exp[n*x]/(1 + LambertW[-x]), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 06 2017 *)

Crossrefs

Main diagonal of A290824.

Cf. A000312, A207833, A254382.

Sequence in context: A214222 A227459 A372200 * A012628 A012623 A009742

Adjacent sequences: A290837 A290838 A290839 * A290841 A290842 A290843

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 12 2017

Status

approved