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A284585 Expansion of Product_{k>=0} (1 - x^(6*k+1)) in powers of x.

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%I A284585 #16 Apr 09 2017 22:29:26
%S A284585 1,-1,0,0,0,0,0,-1,1,0,0,0,0,-1,1,0,0,0,0,-1,2,-1,0,0,0,-1,2,-1,0,0,0,
%T A284585 -1,3,-2,0,0,0,-1,3,-3,1,0,0,-1,4,-4,1,0,0,-1,4,-5,2,0,0,-1,5,-7,3,0,
%U A284585 0,-1,5,-8,5,-1,0,-1,6,-10,6,-1,0,-1,6,-12,9,-2,0,-1
%N A284585 Expansion of Product_{k>=0} (1 - x^(6*k+1)) in powers of x.
%H A284585 Robert Israel, <a href="/A284585/b284585.txt">Table of n, a(n) for n = 0..10000</a>
%F A284585 a(n) = -(1/n)*Sum_{k=1..n} A284098(k)*a(n-k), a(0) = 1.
%F A284585 a(n) = (-1)^n * A280456(n). - _Robert Israel_, Apr 09 2017
%p A284585 N:= 100: # to get a(0)..a(N)
%p A284585 V:= Vector(N+1):
%p A284585 V[1]:= 1:
%p A284585 for k from 0 to floor((N-1)/6) do
%p A284585 V[6*k+2..N+1]:= V[6*k+2..N+1]+V[1..N-6*k]
%p A284585 od:
%p A284585 seq((-1)^n*V[n+1],n=0..N); # _Robert Israel_, Apr 09 2017
%t A284585 CoefficientList[Series[Product[1 - x^(6*k+1), {k, 0, 79}], {x, 0, 79}], x] (* _Indranil Ghosh_, Mar 29 2017 *)
%Y A284585 Cf. Product_{k>=0} (1 - x^(6*k+m)): this sequence (m=1), A284586 (m=5).
%Y A284585 Cf. A280456.
%K A284585 sign
%O A284585 0,21
%A A284585 _Seiichi Manyama_, Mar 29 2017