A357031 E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^2 / 2.

1, 0, 1, 3, 22, 195, 2131, 28623, 445789, 7982355, 161208976, 3626200743, 89942239861, 2438520508515, 71754865476841, 2277574224716703, 77570723071721938, 2821841221403098995, 109200125293424385271, 4479379126010806153143, 194148151869063307919725

Offset: 0

Author

Seiichi Manyama, Sep 09 2022

Keywords

• nonn

Crossrefs

Cf. A030019, A357032.

Cf. A060311, A357024.

Programs

Mathematica

m = 21; (* number of terms *)
A[_] = 0;
Do[A[x_] = Exp[(Exp[x*A[x]] - 1)^2/2] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)

PARI

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

Formula

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