A367281 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^3)^3.

1, 1, 5, 32, 237, 1906, 16179, 142665, 1294115, 11998349, 113194205, 1083131419, 10486939473, 102548233212, 1011333385507, 10047289999536, 100458873883179, 1010138430187185, 10208244014494347, 103625607305637693, 1056166710786300973

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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

Cf. A002294, A360100, A365150, A367240.

Sequence in context: A053157 A102231 A365181 * A127089 A241769 A208046

Adjacent sequences: A367278 A367279 A367280 * A367282 A367283 A367284

Keyword

nonn

Author

Seiichi Manyama, Nov 12 2023

Status

approved