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%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
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