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A367281
G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^3)^3.
1
1, 1, 5, 32, 237, 1906, 16179, 142665, 1294115, 11998349, 113194205, 1083131419, 10486939473, 102548233212, 1011333385507, 10047289999536, 100458873883179, 1010138430187185, 10208244014494347, 103625607305637693, 1056166710786300973
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=2, 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));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 12 2023
STATUS
approved