A356884 E.g.f. satisfies A(x)^A(x) = 1/(1 - x*A(x))^x.

1, 0, 2, 3, 20, 150, 1254, 14280, 190000, 2863728, 49465080, 954312480, 20303200488, 473604468480, 12007399511184, 328671680500800, 9663415159357440, 303695188102656000, 10159173955921651776, 360424299614544829440, 13517056067747847719040

Offset: 0

Author

Seiichi Manyama, Sep 02 2022

Keywords

• nonn

Crossrefs

Cf. A184949, A349559, A356786, A356787, A356885.

Cf. A141209.

Programs

PARI

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

Formula

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