A364984 E.g.f. satisfies A(x) = 1 + x*A(x)^3*exp(x*A(x)).

1, 1, 8, 117, 2596, 77705, 2936406, 134228059, 7204913528, 444331053873, 30963240318250, 2406301353714731, 206354828717754036, 19357367027097743449, 1971809610601104110942, 216754216326949771274715, 25575749384428387961718256, 3224227609551980271408565985

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

Prog

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

Crossrefs

Cf. A364983, A364985, A364986.

Cf. A108447.

Sequence in context: A085699 A046914 A376124 * A341197 A342182 A194494

Adjacent sequences: A364981 A364982 A364983 * A364985 A364986 A364987

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2023

Status

approved