A367233 G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x))^3.

1, 1, 6, 39, 284, 2223, 18267, 155445, 1358073, 12111306, 109802183, 1009001571, 9376972698, 87978198364, 832223905371, 7928413841673, 76002832317437, 732578811761670, 7095717550127526, 69029297500888522, 674181392461483212, 6607910786529613248

Offset

0,3

Links

Table of n, a(n) for n=0..21.

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=3, u=1) = 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. A161797, A365113, A365150.

Sequence in context: A153392 A253077 A231482 * A122827 A103194 A009018

Adjacent sequences: A367230 A367231 A367232 * A367234 A367235 A367236

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2023

Status

approved