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A367239
G.f. satisfies A(x) = 1 + x*A(x) / (1 - x*A(x)^2)^3.
3
1, 1, 4, 19, 104, 615, 3829, 24728, 164122, 1112641, 7671781, 53634389, 379305155, 2708686547, 19505022538, 141470864166, 1032587621470, 7578835132264, 55901583657799, 414157062713599, 3080581445049863, 22996511364853472, 172230640045929990
OFFSET
0,3
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).
PROG
(PARI) a(n, s=3, t=1, u=2) = 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));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 11 2023
STATUS
approved