%I #15 Jul 10 2017 06:49:38

%S 1,12,252,5664,133356,3224952,79387488,1978996416,49797787788,

%T 1262193008556,32177428972632,824182154521056,21193138994244960,

%U 546767126418119352,14146104826919725632,366887630982365262144,9535791498480146879436

%N Coefficients in expansion of 1/E_2^(1/2).

%H Seiichi Manyama, <a href="/A289565/b289565.txt">Table of n, a(n) for n = 0..701</a>

%F G.f.: Product_{n>=1} (1-q^n)^(-A288968(n)/2).

%F a(n) ~ c / (sqrt(n) * r^n), where r = A211342 = 0.03727681029645165815098078565... is the root of the equation Sum_{k>=1} A000203(k) * r^k = 1/24 and c = 0.535261044779387956394739769118415667289349331646288208543596374426... - _Vaclav Kotesovec_, Jul 09 2017

%t nmax = 20; CoefficientList[Series[(1 - 24*Sum[DivisorSigma[1, k]*x^k, {k, 1, nmax}])^(-1/2), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 09 2017 *)

%Y 1/E_k^(1/2): this sequence (k=2), A289566 (k=4), A289567 (k=6), A001943 (k=8), A289568 (k=10), A289569 (k=14).

%Y Cf. A288816 (1/E_2), A288968, A289291 (E_2^(1/2)).

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 08 2017