A381830 G.f. A(x) satisfies A(x) = C(x*A(x)^2) / (1 - x*A(x)), where C(x) is the g.f. of A000108.
1, 2, 10, 69, 558, 4946, 46506, 455587, 4599494, 47517909, 499933964, 5337957532, 57694565830, 630010984557, 6939976239376, 77027050722166, 860564349616694, 9670164031087137, 109221767288604000, 1239281689627682221, 14119315749935075540, 161460732437631678114
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(2*n, n-k)/(n+3*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(n+3*k+1,k) * binomial(2*n,n-k)/(n+3*k+1).