A305991 Expansion of (1-27*x)^(1/9).

1, -3, -36, -612, -11934, -250614, -5513508, -125235396, -2911722957, -68910776649, -1653858639576, -40143659706072, -983519662798764, -24285370135261788, -603664914790793016, -15091622869769825400, -379177024602966863175, -9568643738510163782475

Offset: 0

Author

Seiichi Manyama, Jun 16 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..700

Crossrefs

Cf. A003557, A007947.

(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), this sequence (b=27), A004996 (b=36), A303007 (b=240), A303055 (b=504), A305886 (b=1728).

Programs

PARI

N=20; x='x+O('x^N); Vec((1-27*x)^(1/9))

Formula

a(n) = 3^n/n! * Product_{k=0..n-1} (9*k - 1) for n > 0.

a(n) ~ 27^n / (Gamma(-1/9) * n^(10/9)). - Vaclav Kotesovec, Jun 16 2018

D-finite with recurrence: n*a(n) +3*(-9*n+10)*a(n-1)=0. - R. J. Mathar, Jan 16 2020