A289062 Coefficients in expansion of E_2^12/Product_{k>=1} (1-q^k)^24.

1, -264, 30564, -2012800, 81099090, -1952940672, 22697326712, 63468624384, -4486982088465, 11373493964160, 616923039055284, -663002527580928, -77516928995402226, -352040146340083200, 5929423960701095640, 87636971447313802240, 269600086946598203619

Offset: 0

Author

Seiichi Manyama, Jun 23 2017

Keywords

• sign

Examples

			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 + ... .
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..5000 (terms 0..1000 from Seiichi Manyama)

Crossrefs

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

Programs

Mathematica

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 *)

Formula

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

a(n) ~ exp(4*Pi*sqrt(n)) * n^(21/4) / sqrt(2). - Vaclav Kotesovec, Jul 09 2017