A367232 G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x))^2.

1, 1, 5, 29, 189, 1325, 9757, 74429, 583037, 4662653, 37911037, 312457469, 2604534269, 21919435517, 185992729085, 1589480795133, 13668519794685, 118188894992381, 1026965424910333, 8962634482450429, 78528344593006589, 690502653622083581

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=2, 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. A000108, A011270, A109081.

Sequence in context: A137573 A234317 A346845 * A078945 A113713 A142980

Adjacent sequences: A367229 A367230 A367231 * A367233 A367234 A367235

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2023

Status

approved