A367233 G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x))^3.
1, 1, 6, 39, 284, 2223, 18267, 155445, 1358073, 12111306, 109802183, 1009001571, 9376972698, 87978198364, 832223905371, 7928413841673, 76002832317437, 732578811761670, 7095717550127526, 69029297500888522, 674181392461483212, 6607910786529613248
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..983
Programs
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PARI
a(n, s=3, t=3, u=1) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
Formula
If g.f. satisfies A(x) = 1 + x*A(x)^t / (1 - x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(n+(s-1)*k-1,n-k) / (t*k+u*(n-k)+1).