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%I #19 Oct 21 2023 11:08:16
%S 1,2,-16,212,-3400,60384,-1142960,22598832,-461250208,9644611008,
%T -205537131008,4447969973888,-97482797466624,2159242220999936,
%U -48260706692535552,1087076798266594048,-24652590023639251456,562396337623786449920
%N G.f. satisfies A(x) = 1 + x/A(x)^3*(1 + 1/A(x)^2).
%F G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A363380.
%F a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(4*n+2*k-2,n-1) for n > 0.
%F a(n) ~ c*(-1)^(n-1)*256^n*27^(-n)*3F2([-n, 2*n, 2*n-1/2], [3*n/2, (3*n+1)/2], -1)*n^(-3/2), with c = (1/8)*sqrt(3/(2*Pi)). - _Stefano Spezia_, Oct 21 2023
%o (PARI) a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(4*n+2*k-2, n-1))/n);
%Y Cf. A364393, A364395, A364397.
%Y Cf. A364398, A364400.
%Y Cf. A363380.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jul 22 2023
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