A379172 - OEIS

%I #10 Dec 17 2024 10:12:27

%S 1,4,33,358,4445,59745,846023,12430941,187753479,2896929975,

%T 45465112431,723520554096,11647721390271,189352106241567,

%U 3104046096391902,51254005259550753,851674902290491936,14231191062537888864,238978853442142491358,4030889937027642017872

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

%F a(n) = Sum_{k=0..n} binomial(n+2*k+1,k) * binomial(4*n+5*k+2,n-k)/(n+2*k+1).

%o (PARI) a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(4*n+5*k+2, n-k)/(n+2*k+1));

%Y Cf. A365764, A369215, A379171.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 17 2024