A356892 - OEIS

%I #38 Sep 12 2022 03:05:12

%S 1,0,0,0,24,60,120,210,101136,1089144,7409520,39917790,4097460840,

%T 100410712116,1474154203704,16356956618730,786764261166240,

%U 30867868254267120,778327514455987296,14658714575197061814,522720977799308061240,25075479032600008569900

%N E.g.f. satisfies log(A(x)) = x^3 * (exp(x * A(x)) - 1) * A(x).

%F a(n) = n! * Sum_{k=0..floor(n/4)} (n-2*k+1)^(k-1) * Stirling2(n-3*k,k)/(n-3*k)!.

%t m = 22; (* number of terms *)

%t A[_] = 0;

%t Do[A[x_] = Exp[x^3*(Exp[x*A[x]] - 1)*A[x]] + O[x]^m // Normal, {m}];

%t CoefficientList[A[x], x]*Range[0, m-1]! (* _Jean-François Alcover_, Sep 12 2022 *)

%o (PARI) a(n) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*stirling(n-3*k, k, 2)/(n-3*k)!);

%Y Cf. A349557, A356785, A355508.

%Y Cf. A356963.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Sep 07 2022