A379995 - OEIS

%I #14 Jan 08 2025 12:20:43

%S 1,6,48,476,5608,76372,1179016,20332580,387225120,8068825988,

%T 182564048824,4456476380644,116724944900272,3264981100202564,

%U 97130013288324552,3062011655207131748,101963095705628194624,3576126056313566090500,131762871920106615643480

%N Expansion of e.g.f. exp(-2*x)/(exp(-x) - x)^4.

%F a(n) = n! * Sum_{k=0..n} (k+2)^(n-k) * binomial(k+3,3)/(n-k)!.

%F a(n) ~ n! * n^3 / (6 * (LambertW(1) + 1)^4 * LambertW(1)^(n+2)). - _Vaclav Kotesovec_, Jan 08 2025

%o (PARI) a(n) = n!*sum(k=0, n, (k+2)^(n-k)*binomial(k+3, 3)/(n-k)!);

%Y Cf. A379943, A379993, A379994, A379996.

%Y Cf. A358738.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Jan 07 2025