A289293 - OEIS

%I #18 Mar 05 2018 09:46:27

%S 1,-252,-40068,-10158624,-3362961924,-1254502939032,-502480721822688,

%T -211053631376919744,-91717692784641665028,-40892713821496126310364,

%U -18600635229558474625901928,-8597703758971125751979122656

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

%H Seiichi Manyama, <a href="/A289293/b289293.txt">Table of n, a(n) for n = 0..367</a>

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

%F 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

%t terms = 12;

%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];

%t E6[x]^(1/2) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 23 2018 *)

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

%Y Cf. A013973 (E_6), A288851.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jul 02 2017