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%I #16 Oct 15 2023 09:25:51
%S 1,0,0,0,1,3,6,10,18,39,91,204,435,919,1992,4434,9947,22215,49455,
%T 110480,248505,561930,1273610,2889666,6566736,14959083,34163511,
%U 78182700,179201199,411325125,945512784,2176710450,5018195400,11583688995,26770164919
%N G.f. A(x) satisfies A(x) = 1 + x^4 * (A(x) / (1 - x))^3.
%F a(n) = Sum_{k=0..floor(n/4)} binomial(n-k-1,n-4*k) * binomial(3*k,k) / (2*k+1).
%o (PARI) a(n) = sum(k=0, n\4, binomial(n-k-1, n-4*k)*binomial(3*k, k)/(2*k+1));
%Y Partial sums give A364552.
%Y Cf. A000245, A213282, A361932.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Oct 15 2023
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