A361881 Expansion of 1/(1 - 9*x/(1 + x))^(1/3).

1, 3, 15, 93, 618, 4278, 30390, 219810, 1611105, 11929395, 89045079, 669018837, 5053759440, 38350056072, 292147584072, 2233020788184, 17117923408746, 131560216858110, 1013413369611606, 7822237588031586, 60487791859818348, 468511159492134516

Offset

0,2

Links

Winston de Greef, Table of n, a(n) for n = 0..1103

Formula

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

a(0) = 1; a(n) = (3/n) * Sum_{k=0..n-1} (-1)^(n-1-k) * (n+2*k) * a(k).

n*a(n) = (7*n-4)*a(n-1) + 8*(n-2)*a(n-2) for n > 1.

a(n) ~ 3^(2/3) * 2^(3*n-1) / (Gamma(1/3) * n^(2/3)). - Vaclav Kotesovec, Mar 28 2023

a(n) = (-1)^(1 - n)*3*hypergeom([1 - n, 4/3], [2], 9) for n >= 1. - Peter Luschny, Mar 30 2023

Maple

a := n -> if n = 0 then 1 else (-1)^(1-n)*3*hypergeom([1 - n, 4/3], [2], 9) fi:
seq(simplify(a(n)), n = 0..21); # Peter Luschny, Mar 30 2023

Prog

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

Crossrefs

Cf. A004987, A180400, A361841, A361842, A361882.

Cf. A361375.

Sequence in context: A020108 A323696 A231657 * A303558 A193661 A192296

Adjacent sequences: A361878 A361879 A361880 * A361882 A361883 A361884

Keyword

nonn

Author

Seiichi Manyama, Mar 28 2023

Status

approved