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%I #6 Jun 18 2017 14:45:44
%S 1,-1,-1,1,0,0,-1,0,0,1,1,0,0,0,0,0,-1,0,0,-1,1,-1,2,0,-1,0,0,-2,-1,1,
%T 0,1,0,1,1,0,0,1,0,-1,-1,0,0,1,0,-1,0,0,0,1,0,1,-1,0,-1,0,1,-1,-1,0,0,
%U 0,0,-1,0,-1,1,0,0,1,0,0,2,-1,0,1,1,0,0,-1,0,0,-1,-1,0,-1,0,2,1,0,-1,2,0,0,0,0,1,0,0,-1,-1,-1,0,0,0
%N Expansion of f(-x, -x^7) * f(-x^2, -x^6) in powers of x where f(,) is Ramanujan's two-variable theta function.
%H G. C. Greubel, <a href="/A143251/b143251.txt">Table of n, a(n) for n = 0..1000</a>
%F Euler transform of period 8 sequence [ -1, -1, 0, 0, 0, -1, -1, -2, ...].
%F G.f.: Product_{k>0} (1 - x^(8*k))^2 * (1 - x^(8*k - 1)) * (1 - x^(8*k - 2)) * (1 - x^(8*k - 6)) * (1 - x^(8*k - 7)).
%e q^13 - q^29 - q^45 + q^61 - q^109 + q^157 + q^173 - q^269 - q^317 + ...
%t f[x_, y_] := QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; A143251[n_] := SeriesCoefficient[f[-x, -x^7]*f[-x^2, -x^6], {x, 0, n}]; Table[A143251[n], {n,0,50}] (* _G. C. Greubel_, Jun 18 2017 *)
%o (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k)^([2, 1, 1, 0, 0, 0, 1, 1][k%8 + 1]), 1 + x * O(x^n)), n))}
%K sign
%O 0,23
%A _Michael Somos_, Aug 01 2008
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