A363356 E.g.f. satisfies A(x) = exp(x * A(x) * (1 + x * A(x)^3)).

1, 1, 5, 52, 821, 17536, 473497, 15476224, 594230345, 26221431808, 1307680266221, 72739285725184, 4465197522732157, 299855584017743872, 21867349264346912705, 1721013285639521959936, 145394112130209844644113, 13123788855563296766427136

Offset: 0

Author

Seiichi Manyama, Aug 17 2023

Keywords

• nonn

Crossrefs

Cf. A088695, A362771, A363355.

Cf. A365013.

Programs

PARI

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

Formula

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