A366236 G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^2*A(x)^2.
1, 2, 6, 25, 110, 520, 2566, 13073, 68244, 363129, 1962304, 10739914, 59411546, 331652408, 1865903040, 10569319231, 60227702736, 345015430415, 1985747398748, 11477353063881, 66590427901454, 387685469752989, 2264180109124196, 13261401158297918
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(3*k+1, n-k)*binomial(2*k, k)/(k+1));
Formula
G.f.: 2*(1+x) / (1 + sqrt(1-4*x*(1+x)^3)).
a(n) = Sum_{k=0..n} binomial(3*k+1,n-k) * binomial(2*k,k)/(k+1).