A357029 E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2).

1, 0, 0, 6, 36, 210, 3870, 70224, 1122072, 23086344, 586910880, 15469437456, 441107126856, 14206113541152, 496333927370736, 18463733657766144, 739328759822848320, 31759148433997889280, 1447876893211813379520, 69881726567495477445120

Offset: 0

Author

Seiichi Manyama, Sep 09 2022

Keywords

• nonn

Crossrefs

Cf. A001761, A357028.

Cf. A353344, A357037.

Programs

Mathematica

m = 20; (* number of terms *)
A[_] = 0;
Do[A[x_] = 1/(1 - x*A[x])^(Log[1 - x*A[x]]^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\3, (3*k)!*(n+1)^(k-1)*abs(stirling(n, 3*k, 1))/k!);

Formula

E.g.f. satisfies log(A(x)) = -log(1 - x * A(x))^3.

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n+1)^(k-1) * |Stirling1(n,3*k)|/k!.