A371915 G.f. A(x) satisfies A(x) = 1 - x/A(x)^2 * (1 - A(x) - A(x)^5).
1, 1, 4, 17, 80, 414, 2289, 13199, 78306, 474630, 2926744, 18304543, 115837726, 740379722, 4772461321, 30989448116, 202518745795, 1330961476358, 8791022012712, 58325109518331, 388523983047285, 2597516226459845, 17423367396517210, 117223205014488833
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, sum(k=0, n, binomial(n, k)*binomial(3*n-5*k, n-k-1))/n);
Formula
a(n) = (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(3*n-5*k,n-k-1) for n > 0.