A357028 E.g.f. satisfies A(x) = (1 - x * A(x))^log(1 - x * A(x)).

1, 0, 2, 6, 82, 820, 13568, 235368, 5111748, 123205248, 3404436312, 103998026880, 3516027852456, 129715202957184, 5198615642907360, 224652658604613120, 10419411912935774736, 516120552745366247424, 27198524267826237745824

Offset: 0

Author

Seiichi Manyama, Sep 09 2022

Keywords

• nonn

Crossrefs

Cf. A001761, A357029.

Cf. A357036.

Programs

Mathematica

m = 20; (* number of terms *)
A[_] = 0;
Do[A[x_] = (1 - x*A[x])^Log[1 - x*A[x]] + 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)*abs(stirling(n, 2*k, 1))/k!);

Formula

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

a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n+1)^(k-1) * |Stirling1(n,2*k)|/k!.