A289350 Coefficients in expansion of E_2/Product_{k>=1} (1-q^k)^2.

1, -22, -115, -350, -940, -2124, -4615, -9130, -17575, -32100, -57239, -98512, -166595, -274350, -445055, -708124, -1112002, -1719410, -2629450, -3970230, -5937238, -8785502, -12889630, -18741250, -27045445, -38724088, -55074057, -77791320, -109215025

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Formula

G.f.: Product_{k>=1} (1-q^k)^(A288995(k)/12).

a(n) ~ -3^(1/4) * exp(2*Pi*sqrt(n/3)) / n^(1/4). - Vaclav Kotesovec, Jul 08 2017

Mathematica

nmax = 50; CoefficientList[Series[(1 - 24*Sum[DivisorSigma[1, k]*x^k, {k, 1, nmax}]) / Product[(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 08 2017 *)

Crossrefs

E_2^(m/2)/Product_{k>=1} (1-q^k)^m: A289344 (m=1), this sequence (m=2), A289062 (m=24).

Cf. A006352 (E_2), A066186, A288995.

Sequence in context: A374026 A074277 A299580 * A100930 A260810 A274610

Adjacent sequences: A289347 A289348 A289349 * A289351 A289352 A289353

Keyword

sign

Author

Seiichi Manyama, Jul 03 2017

Status

approved