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Coefficients in expansion of E_2^12/Product_{k>=1} (1-q^k)^24.
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%I #29 Jul 09 2017 09:04:52

%S 1,-264,30564,-2012800,81099090,-1952940672,22697326712,63468624384,

%T -4486982088465,11373493964160,616923039055284,-663002527580928,

%U -77516928995402226,-352040146340083200,5929423960701095640,87636971447313802240,269600086946598203619

%N Coefficients in expansion of E_2^12/Product_{k>=1} (1-q^k)^24.

%H Vaclav Kotesovec, <a href="/A289062/b289062.txt">Table of n, a(n) for n = 0..5000</a> (terms 0..1000 from Seiichi Manyama)

%F G.f.: Product_{k>=1} (1-q^k)^A288995(k).

%F a(n) ~ exp(4*Pi*sqrt(n)) * n^(21/4) / sqrt(2). - _Vaclav Kotesovec_, Jul 09 2017

%e G.f.: (1-q)^264 * (1-q^2)^4152 * (1-q^3)^77064 * ... = 1 - 264*q + 30564*q^2 - 2012800*q^3 + 81099090*q^4 - 1952940672*q^5 + ... .

%t nmax = 20; CoefficientList[Series[(1 - 24*Sum[DivisorSigma[1, k]*x^k, {k, 1, nmax}])^12 / Product[(1 - x^k)^24, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 09 2017 *)

%Y Cf. A000594, A006352 (E_2), A288995, A289063.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jun 23 2017