A375542 - OEIS

%I #6 Sep 01 2024 18:06:31

%S 1,1,8,87,1320,25725,612108,17203851,557748432,20489112729,

%T 841113462420,38160193098159,1896028551663480,102392590090186773,

%U 5971704088187410524,374066073759048220755,25046720079233546922912,1785239641822239101959857,134954928380480636029181220,10784707237797686195626919223

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

%F a(n) ~ 2^n * n^n / (sqrt(1+LambertW(2*exp(-1))) * exp(n) * LambertW(2*exp(-1))^n). - _Vaclav Kotesovec_, Sep 01 2024

%p gf := n -> (-2 - exp(-x))^n:

%p ser := n -> series(gf(n), x, 20):

%p a := n -> expand(n!*coeff(ser(n), x, n)):

%p seq(a(n), n = 0..18);

%t Table[n!*SeriesCoefficient[(-2 - E^(-x))^n,{x,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Sep 01 2024 *)

%K nonn

%O 0,3

%A _Peter Luschny_, Sep 01 2024