A365010 E.g.f. satisfies A(x) = 1 + x*exp(-x)*A(x)^3.

1, 1, 4, 39, 596, 12365, 324714, 10329655, 386190328, 16597810233, 806356830230, 43700423019011, 2613919719004692, 171053575111641157, 12156558707970920866, 932424974682447304815, 76772968644326739801584, 6754080601542663692950769

Offset: 0

Author

Seiichi Manyama, Aug 15 2023

Keywords

• nonn

Crossrefs

Cf. A295239, A302397, A365011.

Cf. A001764, A364983.

Programs

Maple

A365010 := proc(n)
    add( (-k)^(n-k)*A001764(k)/(n-k)!,k=0..n) ;
    %*n! ;
end proc:
seq(A365010(n),n=0..80); # R. J. Mathar, Aug 16 2023

PARI

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

Formula

a(n) = n! * Sum_{k=0..n} (-k)^(n-k) * A001764(k)/(n-k)!.