A289293 Coefficients in expansion of E_6^(1/2).

1, -252, -40068, -10158624, -3362961924, -1254502939032, -502480721822688, -211053631376919744, -91717692784641665028, -40892713821496126310364, -18600635229558474625901928, -8597703758971125751979122656

Offset: 0

Author

Seiichi Manyama, Jul 02 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..367

Crossrefs

E_k^(1/2): A289291 (k=2), A289292 (k=4), this sequence (k=6), A004009 (k=8), A289294 (k=10), A289295 (k=14).

Cf. A013973 (E_6), A288851.

Programs

Mathematica

terms = 12;
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E6[x]^(1/2) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 23 2018 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^(A288851(n)/2).

a(n) ~ c * exp(2*Pi*n) / n^(3/2), where c = -3*sqrt(2)*Pi^(3/2) / (16*Gamma(3/4)^8) = -0.2903826839827320330247215149377503818798115... - Vaclav Kotesovec, Jul 02 2017, updated Mar 05 2018