A356970 E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^2 * A(x)).

1, 0, 0, 6, 12, 40, 1980, 16128, 136080, 4224960, 70943040, 1087178400, 31274100000, 784834652160, 18115033128192, 565994928945600, 18161466717139200, 560655551681971200, 20108422243585658880, 769928646324249699840, 29464638272901949824000

Offset: 0

Author

Seiichi Manyama, Sep 07 2022

Keywords

• nonn

Crossrefs

Cf. A184949, A349556, A356971.

Cf. A356967.

Programs

Mathematica

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

PARI

a(n) = n!*sum(k=0, n\3, (n-k+1)^(k-1)*abs(stirling(n-2*k, k, 1))/(n-2*k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-k+1)^(k-1) * |Stirling1(n-2*k,k)|/(n-2*k)!.