A365119 G.f. satisfies A(x) = (1 + x / (1 - x*A(x)))^3.

1, 3, 6, 19, 69, 267, 1093, 4629, 20142, 89473, 404076, 1849746, 8563558, 40025574, 188612388, 895115942, 4274453904, 20523807009, 99025615998, 479874362583, 2334582421497, 11398055887003, 55828060595832, 274254002718255, 1350907899813921, 6670789629569022

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

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

Prog

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

Crossrefs

Cf. A001006, A365118.

Sequence in context: A058818 A184937 A215817 * A269306 A326317 A306522

Adjacent sequences: A365116 A365117 A365118 * A365120 A365121 A365122

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2023

Status

approved