A365057 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x/2 * A(x)^2)).

1, 1, 6, 70, 1242, 29766, 901108, 33007500, 1419955260, 70189326748, 3920638941576, 244244850932424, 16790688671875000, 1262666306235233160, 103110586277262570672, 9086730135842989237456, 859557307380692050631952, 86872483166310571406250000

Offset

0,3

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A091485, A365058.

C. A363358.

Sequence in context: A024489 A354328 A036361 * A182563 A211036 A284215

Adjacent sequences: A365054 A365055 A365056 * A365058 A365059 A365060

Keyword

nonn

Author

Seiichi Manyama, Aug 19 2023

Status

approved