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 A289294 Coefficients in expansion of E_10^(1/2). 7

%I #20 Mar 05 2018 07:16:51

%S 1,-132,-76428,-12686784,-4629945804,-1581036186312,-643032851554368,

%T -264454897726360704,-114830224962140965068,-50847479367845783084484,

%U -23070238839261012248537688,-10629338992044523324726971456

%N Coefficients in expansion of E_10^(1/2).

%H Seiichi Manyama, <a href="/A289294/b289294.txt">Table of n, a(n) for n = 0..367</a>

%F G.f.: Product_{n>=1} (1-q^n)^(A289024(n)/2).

%F a(n) ~ c * exp(2*Pi*n) / n^(3/2), where c = -3^(3/2) * Pi^(5/2) / (2^(9/2) * Gamma(3/4)^12) = -0.3503612261281732359954402284478780636268623476628... - _Vaclav Kotesovec_, Jul 02 2017, updated Mar 05 2018

%t nmax = 20; s = 10; 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), this sequence (k=10), A289295 (k=14).

%Y Cf. A013974 (E_10), A289024.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jul 02 2017

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Last modified September 18 19:41 EDT 2024. Contains 376002 sequences. (Running on oeis4.)