A357031 - OEIS

%I #14 Sep 12 2022 05:21:40

%S 1,0,1,3,22,195,2131,28623,445789,7982355,161208976,3626200743,

%T 89942239861,2438520508515,71754865476841,2277574224716703,

%U 77570723071721938,2821841221403098995,109200125293424385271,4479379126010806153143,194148151869063307919725

%N E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^2 / 2.

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

%t m = 21; (* number of terms *)

%t A[_] = 0;

%t Do[A[x_] = Exp[(Exp[x*A[x]] - 1)^2/2] + O[x]^m // Normal, {m}];

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

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

%Y Cf. A030019, A357032.

%Y Cf. A060311, A357024.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Sep 09 2022