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A367238
G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x)^2)^2.
3
1, 1, 5, 31, 219, 1672, 13439, 112043, 960017, 8402085, 74791408, 675033956, 6163120105, 56820187321, 528231686315, 4946304326883, 46609889424547, 441664236745594, 4205848369345681, 40228631544942031, 386317524696654392, 3723196299965400616
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=2, t=3, 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