A303007 Expansion of (1-240*x)^(1/8).

1, -30, -3150, -472500, -81506250, -15160162500, -2956231687500, -595469525625000, -122815589660156250, -25791273828632812500, -5493541325498789062500, -1183608449221102734375000, -257434837705589844726562500, -56437637496994696728515625000

Offset: 0

Author

Seiichi Manyama, Jun 15 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..421

Crossrefs

Cf. A003557, A007947, A049210, A108091.

(1-b*x)^(1/A003557(b)): A002420 (b=4), A004984 (b=8), A004990 (b=9), (-1)^n * A108735 (b=12), A301271 (b=16), (-1)^n * A108733 (b=18), A049393 (b=25), A004996 (b=36), this sequence (b=240), A303055 (b=504), A305886 (b=1728).

Programs

Mathematica

CoefficientList[Series[Surd[1-240x,8],{x,0,20}],x] (* Harvey P. Dale, Aug 29 2024 *)

PARI

N=20; x='x+O('x^N); Vec((1-240*x)^(1/8))

Formula

a(n) = 30^n/n! * Product_{k=0..n-1} (8*k - 1) for n > 0.

a(n) = 15^n * A301271(n).

a(n) ~ -2^(4*n - 3) * 15^n / (Gamma(7/8) * n^(9/8)). - Vaclav Kotesovec, Jun 16 2018

D-finite with recurrence: n*a(n) +30*(-8*n+9)*a(n-1)=0. - R. J. Mathar, Jan 20 2020