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Coefficients in expansion of 1/E_6^(3/2).
4

%I #22 Mar 05 2018 08:06:12

%S 1,756,501228,311671584,187266950892,110121960638088,

%T 63808586297102304,36578013578688141504,20797655630223547290348,

%U 11749541312124028845092052,6603568491137827506152966712,3695593478842608407829235523808

%N Coefficients in expansion of 1/E_6^(3/2).

%H Seiichi Manyama, <a href="/A289570/b289570.txt">Table of n, a(n) for n = 0..365</a>

%F G.f.: Product_{n>=1} (1-q^n)^(-3*A288851(n)/2).

%F a(n) ~ c * exp(2*Pi*n) * sqrt(n), where c = 2^(17/2) * Gamma(3/4)^24 / (27 * Pi^(13/2)) = 1.0344943380746471723299237298670710161068814236907171661035... - _Vaclav Kotesovec_, Jul 09 2017, updated Mar 05 2018

%t nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(-3/2), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 09 2017 *)

%Y E_6^(k/12): this sequence (k=-18), A000706 (k=-12), A289567 (k=-6), A109817 (k=1), A289325 (k=2), A289326 (k=3), A289327 (k=4), A289328 (k=5), A289293 (k=6), A289345 (k=7), A289346 (k=8), A289347 (k=9), A289348 (k=10), A289349 (k=11).

%Y Cf. A288851.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 08 2017