A289393 Coefficients in expansion of E_2^(3/4).

1, -18, -108, -936, -13194, -224424, -4218264, -84318336, -1759467636, -37903487130, -836893437912, -18844318997496, -431163494289720, -9997357777073064, -234430475682110256, -5550426839122171776, -132513976699508759994

Offset: 0

Author

Seiichi Manyama, Jul 05 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..703

Crossrefs

E_2^(k/4): A289392 (k=1), A289291 (k=2), this sequence (k=3).

Cf. A006352 (E_2), A289394.

Programs

Mathematica

nmax = 20; CoefficientList[Series[(1 - 24*Sum[DivisorSigma[1, k]*x^k, {k, 1, nmax}])^(3/4), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 08 2017 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^(3*A289394(n)).

a(n) ~ c / (n^(7/4) * r^n), where r = A211342 = 0.03727681029645165815098078565... is the root of the equation Sum_{k>=1} A000203(k) * r^k = 1/24 and c = -0.22385630328806525639758543854251232523806175231599584032442913209... - Vaclav Kotesovec, Jul 08 2017