A365285 E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^3*A(x)).

1, 1, 2, 6, 48, 480, 5040, 57960, 806400, 13426560, 250992000, 5102697600, 113283878400, 2760905347200, 73287883468800, 2093750122464000, 63947194517606400, 2082970788291993600, 72182922107859763200, 2651026034089585152000

Offset: 0

Author

Seiichi Manyama, Aug 31 2023

Keywords

• nonn

Crossrefs

Cf. A358065, A365286, A365287.

Cf. A365282.

Programs

PARI

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

Formula

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