A349023 - OEIS

%I #11 Nov 06 2021 09:09:07

%S 1,2,11,64,417,2892,20941,156500,1198049,9346690,74042938,594001236,

%T 4815995027,39399831458,324840184326,2696343599336,22514057175337,

%U 188977375146888,1593661234493561,13495942411592260,114723671513478118,978570384358686064

%N G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^4)^2.

%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=2) = 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, A349024.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 06 2021