A380514 Expansion of e.g.f. exp(x*G(x)^2) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
1, 1, 5, 67, 1537, 50021, 2107021, 108885295, 6665443457, 471522589417, 37843890892021, 3397250515809371, 337267132243022785, 36687625652474612557, 4339368321317331858557, 554467482301151809302151, 76112537023512618262963201, 11170667360636927554290623825, 1745500813880455301486766050917
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, 2*n!*sum(k=0, n-1, binomial(2*n+2*k, k)/((2*n+2*k)*(n-k-1)!)));
Formula
a(n) = 2 * n! * Sum_{k=0..n-1} binomial(2*n+2*k,k)/((2*n+2*k) * (n-k-1)!) for n > 0.