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%I #23 Dec 13 2024 09:40:35
%S 1,1,0,3,-6,28,-105,444,-1897,8338,-37305,169471,-779537,3623500,
%T -16993990,80316081,-382136133,1828896726,-8798796709,42528048930,
%U -206413678447,1005623593109,-4916026689088,24106987842416,-118551374861525,584526569727010,-2888995759466360
%N G.f. A(x) satisfies A(x) = 1 + x/A(x)^3 * (1 - A(x) + A(x)^4).
%F a(n) = (1/n) * Sum_{k=0..n} (-1)^k * binomial(n,k) * binomial(n-4*k,n-k-1) for n > 0.
%o (PARI) a(n) = if(n==0, 1, sum(k=0, n, (-1)^k*binomial(n, k)*binomial(n-4*k, n-k-1))/n);
%Y Cf. A317133, A364759, A377458, A378958, A378920.
%Y Cf. A371890.
%K sign
%O 0,4
%A _Seiichi Manyama_, Dec 12 2024