%I #13 Jul 26 2023 21:00:59
%S 1,2,-8,72,-768,9072,-114240,1502976,-20414208,284083968,-4029438976,
%T 58040074752,-846682968064,12483389708288,-185725854932992,
%U 2784798982701056,-42039464045854720,638415031298588672,-9746180768647217152,149486708349609050112
%N G.f. satisfies A(x) = 1 + x*(1 + 1/A(x)^4).
%F G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A349311.
%F a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(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(n+4*k-2, n-1))/n);
%Y Cf. A364393, A364407, A364409.
%Y Cf. A349311.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jul 23 2023