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%I #33 Mar 24 2018 15:46:24
%S 1,0,-1,0,-1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,-1,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N Expansion of Product_{k >= 1} (1-q^(2*k)).
%C Convolution of A000009 and A010815.
%F Equals convolution inverse of A035363.
%F a(2n) = A010815(n).
%F Conjecture: |a(n)| = A089806(n).
%e G.f. = 1 - x^2 - x^4 + x^10 + x^14 - x^24 - x^30 + x^44 + x^52 - x^70 - ... - _Altug Alkan_, Mar 24 2018
%t nmax = 100; CoefficientList[ Series[Product[(1 - x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 05 2016 *)
%o (PARI) lista(nn) = {q='q+O('q^nn); Vec(eta(q^2))} \\ _Altug Alkan_, Mar 21 2018
%Y Cf. A000009, A010815, A035363, A089806.
%K sign
%O 0
%A _George Beck_, Jul 03 2016
%E Simpler definition from _N. J. A. Sloane_, Mar 24 2018