A356968 E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^3/6 * A(x)).

1, 0, 0, 0, 4, 10, 40, 210, 4144, 40320, 409800, 4527600, 72552480, 1170449280, 19489513680, 338983444800, 6672681818880, 141166715289600, 3149324442700800, 73497460049395200, 1825098639493104000, 47984287767342796800, 1326460667797094860800

Offset: 0

Author

Seiichi Manyama, Sep 06 2022

Keywords

• nonn

Crossrefs

Cf. A184949, A349556, A356967.

Cf. A356753, A356963.

Programs

PARI

a(n) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (n-2*k+1)^(k-1) * |Stirling1(n-3*k,k)|/(6^k * (n-3*k)!).