A377549 E.g.f. satisfies A(x) = 1 + x*A(x)^5*exp(x*A(x)^2).

1, 1, 12, 285, 10444, 520465, 32882406, 2519264797, 227003238792, 23526134771553, 2757165645132010, 360564513170510341, 52053350012338720332, 8222888925567102799441, 1410913077291231960911934, 261306906300110395598900685, 51955790654759866661097707536

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+3*k+1,k)/( (2*n+3*k+1)*(n-k)! ).

Prog

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

Crossrefs

Cf. A364980, A364982, A364985, A365176.

Cf. A377547.

Sequence in context: A009604 A154669 A079519 * A275007 A262733 A296736

Adjacent sequences: A377546 A377547 A377548 * A377550 A377551 A377552

Keyword

nonn

Author

Seiichi Manyama, Oct 31 2024

Status

approved