A379280 - OEIS

%I #12 Dec 20 2024 02:41:08

%S 1,4,38,500,7601,125520,2187736,39608616,737651032,14040612502,

%T 271931510448,5341639974490,106167131932708,2131125360950758,

%U 43142742495766252,879810600033569754,18057207334571432048,372701480245014988624,7731178967720860156743

%N G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^3) * (1 + x*A(x)) )^2.

%F G.f.: B(x)^2 where B(x) is the g.f. of A364333.

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

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

%Y Cf. A379244, A379252, A379283.

%Y Cf. A364333, A379249.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 19 2024