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%I #15 Jan 30 2020 21:29:18
%S 1,-3,-36,-612,-11934,-250614,-5513508,-125235396,-2911722957,
%T -68910776649,-1653858639576,-40143659706072,-983519662798764,
%U -24285370135261788,-603664914790793016,-15091622869769825400,-379177024602966863175,-9568643738510163782475
%N Expansion of (1-27*x)^(1/9).
%H Seiichi Manyama, <a href="/A305991/b305991.txt">Table of n, a(n) for n = 0..700</a>
%F a(n) = 3^n/n! * Product_{k=0..n-1} (9*k - 1) for n > 0.
%F a(n) ~ 27^n / (Gamma(-1/9) * n^(10/9)). - _Vaclav Kotesovec_, Jun 16 2018
%F D-finite with recurrence: n*a(n) +3*(-9*n+10)*a(n-1)=0. - _R. J. Mathar_, Jan 16 2020
%o (PARI) N=20; x='x+O('x^N); Vec((1-27*x)^(1/9))
%Y Cf. A003557, A007947.
%Y (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).
%K sign
%O 0,2
%A _Seiichi Manyama_, Jun 16 2018