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%I #25 May 07 2017 00:56:54
%S 0,-1,-2,-1,-1,2,0,4,1,2,1,2,-4,1,-1,-5,-2,-1,-3,-1,-2,-2,5,0,-1,1,8,
%T 0,3,2,2,2,3,0,4,-7,0,0,2,-3,-8,-2,-1,-3,-2,-4,0,-3,-3,-2,-1,7,-1,0,1,
%U -1,0,12,2,2,0,4,3,4,0,2,4,3,0,5,-12,2,0,1,-1,1,-3,-11,-1,-2,-6,2,-4,-3,-3,-4,-2,1,-5,-3,-3,-2,11,2,-2,-3,2,0,0,3,12,1
%N Coefficients of q in series expansion of Zagier's identity.
%H Robin Chapman, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v7i1r54">Franklin's argument proves an identity of Zagier</a>, Electron. J. Combin. 7 #R54 (2000).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ZagiersIdentity.html">Zagier's Identity</a>
%F Negative of sequence is convolution of A010815 with A046746. - _Michael Somos_, Jan 07 2015
%F a(n) = A067661(n) - A067659(n) [Chapman]. - _George Beck_, May 06 2017
%e G.f. = - x - 2*x^2 - x^3 - x^4 + 2*x^5 + 4*x^7 + x^8 + 2*x^9 + x^10 + ...
%t Flatten[{0, CoefficientList[Series[-Sum[x^(n - 1)*(QPochhammer[x^(n + 1), x]^2/QPochhammer[x^(n), x]), {n, 1, 101}], {x, 0, 100}], x]}] (* _Mats Granvik_, Jan 05 2015 *)
%t a[ n_] := SeriesCoefficient[ Sum[ QPochhammer[ x] - QPochhammer[ x, x, k], {k, 0, n}], {x, 0, n}]; (* _Michael Somos_, Jan 07 2015 *)
%t a[ n_] := SeriesCoefficient[ -Sum[ QPochhammer[ x^k, x] x^k / (1 - x^k)^2, {k, n}], {x, 0, n}]; (* _Michael Somos_, Jan 07 2015 *)
%Y Cf. A046746.
%K sign
%O 0,3
%A _Eric W. Weisstein_, Mar 29 2006
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