A375607 - OEIS

%I #19 Aug 21 2024 11:22:00

%S 1,1,2,12,72,480,3960,40320,463680,5866560,82857600,1297296000,

%T 22133865600,407869862400,8096683795200,172405968134400,

%U 3915525770956800,94443904345190400,2412049832704512000,65035187612185190400,1845812342328514560000

%N Expansion of e.g.f. 1 / (exp(-x^3) - x).

%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+1)^k/k!.

%F a(n) ~ sqrt(2*Pi) * 3^((n+1)/3) * n^(n + 1/2) / ((1 + LambertW(3)) * exp(n) * LambertW(3)^((n+1)/3)). - _Vaclav Kotesovec_, Aug 21 2024

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x^3)-x)))

%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k+1)^k/k!);

%Y Cf. A072597, A375604.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 21 2024