|
%I #18 Mar 04 2024 04:27:43
%S 1,0,2,3,64,365,7356,85687,1920752,34821369,905128300,22172123171,
%T 672107454888,20552960420005,721088019634724,26257726364294895,
%U 1053711696230404576,44336326818388565105,2010106841636689325532,95747319823049127621019
%N E.g.f. satisfies log(A(x)) = x * (exp(x*A(x)) - 1) * A(x).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(k-1) * Stirling2(n-k,k)/(n-k)!.
%t nmax = 19; A[_] = 1;
%t Do[A[x_] = Exp[x*(Exp[x*A[x]]-1)*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
%t CoefficientList[A[x], x]*Range[0, nmax]! (* _Jean-François Alcover_, Mar 04 2024 *)
%o (PARI) a(n) = n!*sum(k=0, n\2, (n+1)^(k-1)*stirling(n-k, k, 2)/(n-k)!);
%Y Cf. A349560, A356788, A356789.
%Y Cf. A184949, A349557, A355843.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 27 2022
|
