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%I #10 Sep 30 2017 04:46:43
%S 1,-1,0,-1,-1,0,2,1,0,2,-2,1,-1,2,-2,-2,-2,-1,0,2,2,-3,0,1,1,2,2,0,2,
%T -2,0,1,0,-3,2,-2,0,1,-2,-4,-1,1,2,-4,0,2,0,0,0,0,2,3,0,3,0,2,-2,-1,
%U -2,2,-1,0,0,7,2,0,-6,-2,-2,-2,-2,-2,0,-3,0,2,0,0,4,-2,-2,5,-2,-1,1,-2,0,1,2,2,-2,0,2,2,4,-2,4,0,2,0,-2,2,0,-3,0
%N Expansion of q^(-1)eta(q^2)*eta(q^8)^2*eta(q^10)/eta(q^4) in powers of q^2.
%H G. C. Greubel, <a href="/A113423/b113423.txt">Table of n, a(n) for n = 0..1000</a>
%H K. Ono, <a href="http://www.jstor.org/stable/2974471">Ramanujan, taxicabs, birthdates, ZIP codes and twists</a>, Amer. Math. Monthly, 104 (1997), 912-917, MR1490909 (98i:11020).
%F Euler transform of period 20 sequence [ -1, 0, -1, -2, -2, 0, -1, -2, -1, -1, -1, -2, -1, 0, -2, -2, -1, 0, -1, -3, ...].
%e q -q^3 -q^7 -q^9 +2*q^13 +q^15 +2*q^19 -2*q^21 +q^23 +...
%t a[n_] := SeriesCoefficient[QPochhammer[q^2]* QPochhammer[q^8]^2*
%t QPochhammer[q^10]/QPochhammer[q^4], {q, 0, n}]; Table[a[n], {n, 0, 100}][[;; ;; 2]] (* _G. C. Greubel_, Mar 10 2017 *)
%o (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^4+A)^2*eta(x^5+A)/eta(x^2+A), n))}
%K sign
%O 0,7
%A _Michael Somos_, Oct 31 2005
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