A375542 a(n) = n! * [x^n] (-2 - exp(-x))^n.

1, 1, 8, 87, 1320, 25725, 612108, 17203851, 557748432, 20489112729, 841113462420, 38160193098159, 1896028551663480, 102392590090186773, 5971704088187410524, 374066073759048220755, 25046720079233546922912, 1785239641822239101959857, 134954928380480636029181220, 10784707237797686195626919223

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) ~ 2^n * n^n / (sqrt(1+LambertW(2*exp(-1))) * exp(n) * LambertW(2*exp(-1))^n). - Vaclav Kotesovec, Sep 01 2024

Maple

gf := n -> (-2 - exp(-x))^n:
ser := n -> series(gf(n), x, 20):
a := n -> expand(n!*coeff(ser(n), x, n)):
seq(a(n), n = 0..18);

Mathematica

Table[n!*SeriesCoefficient[(-2 - E^(-x))^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 01 2024 *)

Crossrefs

Sequence in context: A378688 A243922 A239753 * A246512 A366233 A248471

Adjacent sequences: A375539 A375540 A375541 * A375543 A375544 A375545

Keyword

nonn

Author

Peter Luschny, Sep 01 2024

Status

approved