A364985 E.g.f. satisfies A(x) = 1 + x*A(x)^3*exp(x*A(x)^2).

1, 1, 8, 123, 2884, 91445, 3664926, 177796759, 10132646840, 663644108169, 49123993335130, 4055804550134051, 369544757016476196, 36834870020525413213, 3987179241476814768854, 465777171342934543710255, 58407238852473276959363056, 7825395596421876706944643985

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(2*n+k+1,k)/( (2*n+k+1)*(n-k)! ).

Prog

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

Crossrefs

Cf. A364983, A364984, A364986.

Cf. A003168.

Sequence in context: A195247 A239755 A264408 * A120957 A302356 A367122

Adjacent sequences: A364982 A364983 A364984 * A364986 A364987 A364988

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2023

Status

approved