A371893 - OEIS

%I #8 Apr 11 2024 10:10:09

%S 1,2,0,16,-32,336,-1472,10944,-63744,441088,-2866688,19772416,

%T -134832128,941381632,-6585720832,46607831040,-331406262272,

%U 2373110628352,-17072541007872,123438375763968,-896088779128832,6530356893777920,-47752086733717504

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

%F a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(3*n-4*k-2,n-1) for n > 0.

%o (PARI) a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(3*n-4*k-2, n-1))/n);

%Y Cf. A364393, A364394, A364396, A364397, A366364.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 11 2024