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%I #33 Feb 21 2021 04:07:00
%S 1,-24,264,-1760,7944,-25872,64416,-133056,253704,-472760,825264,
%T -1297056,1938336,-2963664,4437312,-6091584,8118024,-11368368,
%U 15653352,-19822176,24832944,-32826112,42517728,-51425088,61903776,-78146664,98021616,-115331264,133522752
%N Expansion of eta(q)^24 / eta(q^2)^12 in powers of q.
%H Seiichi Manyama, <a href="/A286346/b286346.txt">Table of n, a(n) for n = 0..10000</a>
%H Simon Plouffe, <a href="http://vixra.org/abs/1409.0048">Conjectures of the OEIS, as of June 20, 2018.</a>
%F a(n) = (-1)^n * A000145(n).
%F Euler Transform of [-24, -12, -24, -12, -24, -12, -24, -12, ...]. - _Simon Plouffe_, Jun 23 2018
%t nmax = 20; CoefficientList[Series[Product[((1 - x^k)/(1 + x^k))^12, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 10 2018 *)
%t a[n_] := (-1)^n SquaresR[12, n];
%t a /@ Range[0, 30] (* _Jean-François Alcover_, Feb 21 2021 *)
%o (PARI) q = 'q + O('q^50); Vec(eta(q)^24 / eta(q^2)^12) \\ _Michel Marcus_, Jul 07 2018
%Y Cf. A000145, A013973 (E_6).
%K sign
%O 0,2
%A _Seiichi Manyama_, May 08 2017
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