A365176 E.g.f. satisfies A(x) = 1 + x*A(x)^4*exp(x*A(x)^2).

1, 1, 10, 195, 5836, 236925, 12177966, 758458603, 55528414264, 4674208189977, 444823048027450, 47227542351423951, 5534636939373353604, 709653811287800826421, 98825110036657191358822, 14853654178825132742729715, 2396666529204491489278153456

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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

Prog

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

Crossrefs

Cf. A364987, A364989, A365175, A365177.

Sequence in context: A187652 A361311 A007816 * A126463 A239766 A294047

Adjacent sequences: A365173 A365174 A365175 * A365177 A365178 A365179

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2023

Status

approved