A365115 G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^5.

1, 1, 5, 20, 90, 440, 2236, 11720, 62960, 344690, 1916170, 10787762, 61380770, 352410760, 2039099640, 11878519460, 69608606348, 410056995475, 2426936098575, 14424334077975, 86055337016695, 515170271387970, 3093724519080210, 18631778892165080

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

If g.f. satisfies A(x) = 1 + x/(1 - x*A(x))^s, then a(n) = Sum_{k=0..n} binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).

Prog

(PARI) a(n, s=5) = sum(k=0, n, binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

Crossrefs

Cf. A000108, A365113, A365114.

Cf. A321799, A365112.

Sequence in context: A192249 A017966 A360076 * A375455 A352149 A196532

Adjacent sequences: A365112 A365113 A365114 * A365116 A365117 A365118

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2023

Status

approved