login
A367242
G.f. satisfies A(x) = 1 + x / (1 - x*A(x)^3)^2.
2
1, 1, 2, 9, 40, 202, 1068, 5884, 33356, 193365, 1140940, 6829601, 41372238, 253156085, 1562416632, 9714660195, 60795387840, 382639224327, 2420498032350, 15380899180204, 98134455984896, 628425763698123, 4037685422823604, 26021345223509038, 168164609160791154
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=0, 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
Cf. A364742.
Sequence in context: A367044 A235596 A346577 * A052512 A166554 A038156
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 11 2023
STATUS
approved