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%I #12 Oct 14 2023 14:00:15
%S 1,1,0,0,1,4,6,4,5,28,84,140,162,304,1018,2644,4760,7364,15540,42680,
%T 102059,195904,356542,782880,1950844,4467288,9011156,17960676,
%U 39984254,94642292,212395260,444063984,931300500,2082762572,4796413292,10681800072,22892593021
%N G.f. A(x) satisfies A(x) = 1 + x + x^4*A(x)^4.
%F a(n) = Sum_{k=0..floor(n/4)} binomial(3*k+1,n-4*k) * binomial(4*k,k)/(3*k+1).
%F a(n) = A366595(n) + A366595(n-1).
%o (PARI) a(n) = sum(k=0, n\4, binomial(3*k+1, n-4*k)*binomial(4*k, k)/(3*k+1));
%Y Cf. A137954, A366267, A366557.
%Y Cf. A366554, A366556.
%Y Cf. A366595.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Oct 13 2023