A365113 G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^3.

1, 1, 3, 9, 31, 114, 438, 1739, 7077, 29364, 123756, 528324, 2279868, 9928679, 43580301, 192601419, 856317717, 3827501985, 17188943523, 77521747638, 350959738842, 1594390493067, 7266093316649, 33209221327752, 152182572790008, 699083290518817, 3218624408121555

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

If g.f. satisfies A(x) = 1 + x/(1 - x*A(x))^s, then a(n) = Sum_{k=0..n} binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).

Prog

(PARI) a(n, s=3) = sum(k=0, n, binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

Crossrefs

Cf. A000108, A365114, A365115.

Cf. A161797, A365110.

Sequence in context: A049179 A049154 A225305 * A110136 A202180 A151034

Adjacent sequences: A365110 A365111 A365112 * A365114 A365115 A365116

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2023

Status

approved