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%I #10 Dec 18 2024 09:26:07
%S 1,4,30,304,3557,45150,604222,8393282,119872890,1749183075,
%T 25964512607,390828464403,5951561595889,91523131078999,
%U 1419293428538496,22169968253466467,348507676062911520,5509187208564734328,87522347516801353980,1396619714730284551913,22375420057050167868366
%N G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * (1 + x*A(x))^3.
%F a(n) = Sum_{k=0..n} binomial(n+2*k+1,k) * binomial(3*n+6*k+3,n-k)/(n+2*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(3*n+6*k+3, n-k)/(n+2*k+1));
%Y Cf. A379172, A379188, A379191.
%Y Cf. A002293, A274735, A364475.
%Y Cf. A198953.
%K nonn,new
%O 0,2
%A _Seiichi Manyama_, Dec 17 2024