A289344 Coefficients in expansion of E_2^(1/2)/Product_{k>=1} (1-q^k).

1, -11, -118, -1473, -23635, -434861, -8659573, -181387821, -3936961298, -87743843970, -1996149058302, -46163368994680, -1082012001849499, -25646334881233711, -613664275728573585, -14803437882920457712, -359626550280367615329

Offset: 0

Author

Seiichi Manyama, Jul 03 2017

Keywords

• sign

Crossrefs

Cf. A006352 (E_2), A288995, A289062, A289291.

Cf. A106205, A106203.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Sqrt[1 - 24*Sum[DivisorSigma[1, k]*x^k, {k, 1, nmax}]] / Product[1 - x^k, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 03 2017 *)

Formula

G.f.: Product_{k>=1} (1-q^k)^(A288995(k)/24).

a(n) ~ c / (n^(3/2) * r^n), where r = A211342 = 0.03727681029645165815098078565... is the root of the equation Sum_{k>=1} A000203(k) * r^k = 1/24 and c = -0.309300289625571303778321676728514880378401177270067457514896529... - Vaclav Kotesovec, Jul 03 2017