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

%S 1,2,15,142,1533,17924,220936,2827218,37202580,500228562,6842899886,

%T 94931338876,1332438761910,18887047322030,269986427261981,

%U 3887654399820062,56337997080499605,821021578186212094,12024687038651388155,176900548019426869808,2612917215947948178941

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

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

%F G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A349333.

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

%Y Cf. A349333, A371379, A371519, A371521, A371522.

%Y Cf. A270386, A371518.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 26 2024