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%I #11 Sep 17 2023 10:05:28
%S 1,0,0,0,1,1,0,0,4,9,5,0,22,78,91,35,140,680,1224,969,1254,5985,14630,
%T 17710,17710,55660,164450,269100,299520,593775,1805076,3681405,
%U 4951692,7594752,20173560,47303520,76404460,110676324,239784864,589602585,1106339923
%N G.f. satisfies A(x) = 1 + x^4*A(x)^4*(1 + x*A(x)).
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(k,n-4*k) * binomial(n+1,k).
%o (PARI) a(n) = sum(k=0, n\4, binomial(k, n-4*k)*binomial(n+1, k))/(n+1);
%Y Cf. A365727, A365728, A365729, A365731.
%Y Cf. A001005, A001006, A365724.
%Y Cf. A215341.
%K nonn
%O 0,9
%A _Seiichi Manyama_, Sep 17 2023
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