login
G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^4)^3.
1

%I #9 Nov 06 2021 09:09:16

%S 1,3,18,124,951,7764,66200,582594,5252133,48254668,450186720,

%T 4253328540,40612877001,391300954065,3799506069816,37142836241690,

%U 365255937037437,3610755090793272,35861607622930556,357670540310182842,3580797575489620740

%N G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^4)^3.

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

%o (PARI) a(n, s=4, t=3) = sum(k=0, n, binomial(t*n-(t-1)*(k-1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

%Y Cf. A118971, A321798, A349023.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 06 2021