A362206 Expansion of 1/(1 - x/(1-9*x)^(1/3)).

1, 1, 4, 25, 181, 1399, 11212, 91936, 765805, 6452449, 54841438, 469306102, 4038193870, 34903997029, 302828905471, 2635745917759, 23003622046900, 201241080558652, 1764149626139119, 15493365042402772, 136288275628625410, 1200600389345625754

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..n} (-9)^k * binomial(-(n-k)/3,k) = Sum_{k=0..n} 9^(n-k) * binomial(n-2*k/3-1,n-k).

a(n) ~ (1-9*r)^(1/3) * (6 - 18*r + r^2) / (109 * r^n), where r = 0.1109593191262346... is the root of the equation r*(9 + r^2) = 1. - Vaclav Kotesovec, Feb 19 2024

Mathematica

Table[Sum[9^(n - k)*Binomial[n - 2*k/3 - 1, n - k], {k, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Feb 19 2024 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-x/(1-9*x)^(1/3)))

Crossrefs

Cf. A026671, A362157, A362210.

Sequence in context: A324169 A213231 A051820 * A364759 A246539 A367017

Adjacent sequences: A362203 A362204 A362205 * A362207 A362208 A362209

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 11 2023

Status

approved