A376803 -id:A376803 - cp's OEIS frontend

A376802 Expansion of 1/((1 - x)^3 - 9*x)^(1/3).

1, 4, 31, 283, 2770, 28204, 294568, 3131650, 33732883, 367035814, 4025600941, 44439461275, 493218155119, 5498860571026, 61543476786067, 691095770653867, 7783168304357434, 87878978740300960, 994484816394177214, 11276915136560900662, 128106749179069022344

Offset: 0

Seiichi Manyama, Oct 04 2024

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..936

Partial sums of A361895.
Cf. A098536, A376803, A376804.
Cf. A376805, A376806.
Cf. A004987.

CoefficientList[Series[1/Surd[((1-x)^3-9x),3],{x,0,30}],x] (* Harvey P. Dale, Dec 11 2024 *)

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

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

a(n) = hypergeom([(1+n)/2, 1+n/2, -n], [2/3, 1], -4/3). - Stefano Spezia, May 04 2025

A376804 Expansion of 1/((1 - x)^3 - 9*x^3)^(1/3).

Original entry on oeis.org

1, 1, 1, 4, 13, 31, 79, 232, 673, 1891, 5401, 15742, 45958, 134122, 393394, 1159432, 3425101, 10137985, 30079405, 89437960, 266389615, 794667325, 2374097485, 7102303240, 21272892055, 63788000461, 191471030791, 575287348546, 1730027151334, 5206918491298

Offset: 0

Seiichi Manyama, Oct 04 2024

nonn

Cf. A098536, A376802, A376803.

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

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

cp's OEIS Frontend

A376802 Expansion of 1/((1 - x)^3 - 9*x)^(1/3).

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