A365115 - OEIS

%I #10 Aug 22 2023 07:57:08

%S 1,1,5,20,90,440,2236,11720,62960,344690,1916170,10787762,61380770,

%T 352410760,2039099640,11878519460,69608606348,410056995475,

%U 2426936098575,14424334077975,86055337016695,515170271387970,3093724519080210,18631778892165080

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

%F 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).

%o (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));

%Y Cf. A000108, A365113, A365114.

%Y Cf. A321799, A365112.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 22 2023