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Coefficients in expansion of E_14^(1/2).
6

%I #18 Mar 05 2018 07:19:57

%S 1,-12,-98388,-20312544,-5889254484,-2083830070392,-810894400450848,

%T -334381509272710464,-143464412162723380308,-63364234685240118242604,

%U -28614423885137875351570248,-13150804531745894256074689056

%N Coefficients in expansion of E_14^(1/2).

%H Seiichi Manyama, <a href="/A289295/b289295.txt">Table of n, a(n) for n = 0..367</a>

%F G.f.: Product_{n>=1} (1-q^n)^(A289029(n)/2).

%F a(n) ~ c * exp(2*Pi*n) / n^(3/2), where c = -9 * Pi^(7/2) / (2^(11/2) * Gamma(3/4)^16) = -0.422728335899452596724927626919867458580193404969719... - _Vaclav Kotesovec_, Jul 02 2017, updated Mar 05 2018

%t nmax = 20; s = 14; CoefficientList[Series[Sqrt[1 - 2*s/BernoulliB[s] * Sum[DivisorSigma[s - 1, k]*x^k, {k, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 02 2017 *)

%Y E_k^(1/2): A289291 (k=2), A289292 (k=4), A289293 (k=6), A004009 (k=8), A289294 (k=10), this sequence (k=14).

%Y Cf. A058550 (E_14), A289029.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jul 02 2017