A371616 G.f. satisfies A(x) = 1 + x / (1 - x*A(x)^3)^3.
1, 1, 3, 15, 82, 495, 3147, 20812, 141621, 985287, 6976369, 50108232, 364202415, 2673756449, 19797659586, 147677816532, 1108711280376, 8371222635096, 63525564996093, 484243596619753, 3706268752629237, 28470703720193010, 219432896755734137
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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PARI
a(n, r=1, s=3, t=0, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
Formula
a(n) = Sum_{k=0..n} binomial(3*(n-k)+1,k) * binomial(n+2*k-1,n-k)/(3*(n-k)+1).