A377531 - OEIS

%I #9 Oct 31 2024 13:28:16

%S 1,0,4,12,96,760,7260,80724,1008112,14079888,216881460,3652767580,

%T 66773963784,1316433381432,27840054610732,628626642921060,

%U 15093709672205280,383989133237230624,10317497504580922212,291958800400148127660,8678485827979443326200

%N Expansion of e.g.f. 1/(1 - x^2 * exp(x))^2.

%F a(n) = n! * Sum_{k=0..floor(n/2)} (k+1) * k^(n-2*k)/(n-2*k)!.

%F a(n) ~ n! * n / ((1 + LambertW(1/2))^2 * 2^(n+2) * LambertW(1/2)^n). - _Vaclav Kotesovec_, Oct 31 2024

%o (PARI) a(n) = n!*sum(k=0, n\2, (k+1)*k^(n-2*k)/(n-2*k)!);

%Y Cf. A358080, A377532.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Oct 31 2024