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%I #29 Sep 08 2022 08:45:12
%S 1,0,0,0,0,-2,0,0,0,0,1,0,0,0,0,-2,0,0,0,0,4,0,0,0,0,-4,0,0,0,0,5,0,0,
%T 0,0,-6,0,0,0,0,9,0,0,0,0,-12,0,0,0,0,13,0,0,0,0,-16,0,0,0,0,21,0,0,0,
%U 0,-26,0,0,0,0,29,0,0,0,0,-36,0,0,0,0,46,0,0,0,0,-54,0,0,0,0,62,0,0,0,0,-74,0
%N Expansion of Product_{k>=1} (1 - q^(10k-5))^2.
%H G. C. Greubel, <a href="/A089814/b089814.txt">Table of n, a(n) for n = 0..5000</a>
%F a(5*n) = A022597(n). a(n) = 0 unless n == 0 (mod 5). - _Michael Somos_, Jun 08 2012
%t A022597[n_] := SeriesCoefficient[ Product[1 + q^k, {k, n}]^-2, {q, 0, n}]; a[n_] := If[Mod[n, 5] != 0, 0, A022597[n/5]]; a[0] = 1; Table[a[n], {n, 0, 96}] (* _Jean-François Alcover_, Nov 12 2012, after _Michael Somos_ *)
%o (PARI) x='x+O(x^100); Vec(prod(k=1,20, (1-x^(10*k-5))^2)) \\ _G. C. Greubel_, Oct 20 2018
%o (Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1-x^(10*k-5))^2: k in [1..20]]))); // _G. C. Greubel_, Oct 20 2018
%Y Cf. A022597 (expansion of Product_{m >= 1} (1 + q^m)^(-2)).
%K sign
%O 0,6
%A _Eric W. Weisstein_, Nov 12 2003
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