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G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^2*A(x)^3.
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%I #9 Oct 05 2023 08:34:54

%S 1,2,8,49,329,2401,18452,147140,1206157,10101011,86047138,743288984,

%T 6495476548,57321239999,510104531479,4572492374150,41247768216331,

%U 374175606700172,3411195598361653,31236732721224722,287182875831208468,2649838553953071239

%N G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^2*A(x)^3.

%F a(n) = Sum_{k=0..n} binomial(4*k+1,n-k) * binomial(3*k,k)/(2*k+1).

%o (PARI) a(n) = sum(k=0, n, binomial(4*k+1, n-k)*binomial(3*k, k)/(2*k+1));

%Y Cf. A364336, A366240, A366241.

%Y Cf. A366221.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 05 2023