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G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1-x))^3.
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%I #11 Mar 26 2024 11:15:11

%S 1,3,24,235,2586,30603,380359,4896753,64731747,873539236,11984536632,

%T 166661420814,2343950447112,33282048811530,476462982915993,

%U 6869620848003570,99663539644072305,1453861111238442363,21312207036239313936,313783619269186619589

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

%F a(n) = 3 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+2,k)/(5*k+3).

%F G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A349333.

%o (PARI) a(n) = 3*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+2, k)/(5*k+3));

%Y Cf. A349333, A371379, A371519, A371521, A371523.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 26 2024