A367280 G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x)^3)^2.
1, 1, 5, 33, 251, 2073, 18069, 163600, 1523731, 14504988, 140499307, 1380322749, 13721269995, 137758098052, 1394840743638, 14227181658075, 146048314214619, 1507739540085350, 15643456882376418, 163036276218805231, 1706021256401103673
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, t=3, u=3) = 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).