A362210 Expansion of 1/(1 - x/(1-9*x)^(2/3)).

1, 1, 7, 58, 505, 4498, 40576, 368965, 3373225, 30958240, 284934754, 2628211291, 24283705558, 224677646416, 2081054132179, 19293026227024, 178996540057615, 1661743445778403, 15435351753092176, 143439377236572826, 1333496145331028230

Offset: 0

Author

Seiichi Manyama, Apr 11 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A362206.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(1/(1-x/(1-9*x)^(2/3)))

Formula

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