A371610 G.f. satisfies A(x) = ( 1 + x * (1 + x*A(x)^3)^2 )^2.
1, 2, 5, 30, 162, 996, 6449, 43086, 296750, 2086244, 14920110, 108202326, 793793106, 5880645408, 43931188235, 330570658228, 2503247547204, 19061888196960, 145874708874538, 1121290880430144, 8653411948545596, 67022656919955620, 520808586384360885
Offset: 0
Keywords
Programs
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PARI
a(n, r=2, s=2, t=0, u=6) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
Formula
a(n) = Sum_{k=0..n} binomial(6*(n-k)+2,k) * binomial(2*k,n-k)/(3*(n-k)+1).
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A137967.