A366221 G.f. A(x) satisfies A(x) = 1 + x*(1 + x)^2*A(x)^3.
1, 1, 5, 25, 145, 905, 5941, 40433, 282721, 2018897, 14661349, 107945993, 803922289, 6045458905, 45840518933, 350100674785, 2690717983169, 20794719218593, 161502488175557, 1259855507859193, 9867012143508305, 77554946281194793, 611575725258403061
Offset: 0
Keywords
Programs
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Mathematica
nmax = 22; A[_] = 1; Do[A[x_] = 1 + x*(1 + x)^2*A[x]^3 + O[x]^(nmax+1) // Normal, {nmax+1}]; CoefficientList[A[x], x] (* Jean-François Alcover, Mar 03 2024 *) -
PARI
a(n) = sum(k=0, n, binomial(2*k, n-k)*binomial(3*k, k)/(2*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(2*k,n-k) * binomial(3*k,k)/(2*k+1).
G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366434.