A365286 E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^3*A(x)^2).

1, 1, 2, 6, 48, 600, 7920, 108360, 1693440, 32114880, 715478400, 17616614400, 467505561600, 13438170345600, 421361740800000, 14345678194848000, 524464774215782400, 20420391682852761600, 844038690729589555200, 36981569420732192256000

Offset: 0

Author

Seiichi Manyama, Aug 31 2023

Keywords

• nonn

Crossrefs

Cf. A358065, A365285, A365287.

Programs

PARI

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

Formula

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