A357024 E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^2.

1, 0, 2, 6, 74, 750, 11402, 195006, 3994202, 93164910, 2455754762, 72098755806, 2333497474970, 82569245246670, 3170700672801482, 131342693516044926, 5837883571730770778, 277151780512413426990, 13997018265350140886282, 749304617892345721184286

Offset: 0

Author

Seiichi Manyama, Sep 09 2022

Keywords

• nonn

Crossrefs

Cf. A030019, A357025.

Cf. A052859, A357009, A357031.

Programs

Mathematica

m = 20; (* number of terms *)
A[_] = 0;
Do[A[x_] = Exp[(Exp[x*A[x]] - 1)^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)/k!);

Formula

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