A365121 G.f. A(x) satisfies A(x) = (1 + x / (1 - x*A(x))^2)^3.
1, 3, 9, 40, 192, 993, 5375, 30081, 172650, 1010640, 6010530, 36214656, 220590082, 1356131892, 8403647454, 52436122717, 329170499604, 2077465903503, 13173914483799, 83897445169341, 536355204428412, 3440875097256529, 22144300030907667
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, t=3) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
Formula
If g.f. satisfies A(x) = (1 + x/(1 - x*A(x))^s)^t, then a(n) = Sum_{k=0..n} binomial(t*(n-k+1),k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).
G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A367242. - Seiichi Manyama, Dec 06 2024