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

Author

Seiichi Manyama, Oct 04 2024

Keywords

• nonn

Links

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

Crossrefs

Partial sums of A361895.

Cf. A098536, A376803, A376804.

Cf. A376805, A376806.

Cf. A004987.

Programs

Mathematica

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

PARI

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

Formula

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