A382893 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^2 * A(x) )^2.
1, 2, 11, 60, 365, 2350, 15767, 109048, 771993, 5567066, 40751267, 302018484, 2261763205, 17088919814, 130108591407, 997225521136, 7688232599089, 59581977618098, 463890112373563, 3626778446099756, 28461425971969693, 224114796803735774, 1770236735807921863
Offset: 0
Keywords
Programs
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PARI
a(n, r=2, s=2, t=3, u=0) = 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
G.f. A(x) satisfies A(x) = ( 1 + x * (1+x)^2 * A(x)^(3/2) )^2.
If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(s*k,n-k)/(t*k+u*(n-k)+r).
G.f.: B(x)^2, where B(x) is the g.f. of A366221.