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G.f. A(x) satisfies A(x) = 1 + x^3 * (A(x) / (1 - x))^4.
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%I #9 Oct 15 2023 09:26:00

%S 1,0,0,1,4,10,24,67,200,586,1704,5049,15232,46284,141240,433696,

%T 1340500,4164830,12993792,40697472,127941300,403561902,1276763096,

%U 4050430502,12882398456,41068966204,131211997496,420056152498,1347272602056,4328764460928,13931034024536

%N G.f. A(x) satisfies A(x) = 1 + x^3 * (A(x) / (1 - x))^4.

%F a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,n-3*k) * binomial(4*k,k) / (3*k+1).

%o (PARI) a(n) = sum(k=0, n\3, binomial(n+k-1, n-3*k)*binomial(4*k, k)/(3*k+1));

%Y Partial sums give A215340.

%Y Cf. A213336, A364410, A366646.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Oct 15 2023