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%I #17 Mar 06 2018 10:55:56
%S 1,-62,8579,-1476538,276299401,-54140398258,10925052030358,
%T -2250028212438240,470403050272649518,-99482921702360817662,
%U 21231436164082720565341,-4564732260005808181200000,987422026920066412423809840
%N Coefficients in expansion of (q*j(q))^(-1/12) where j(q) is the elliptic modular invariant (A000521).
%F Convolution inverse of A289297.
%F a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(3/4), where c = 0.28101701912289268934379724324854717406285519051128823261445... = 2^(1/4) * exp(Pi/(4 * sqrt(3))) * Pi / (3^(1/4) * Gamma(1/4) * Gamma(1/3)^(3/2)). - _Vaclav Kotesovec_, Feb 20 2018, updated Mar 06 2018
%F a(n) * A289297(n) ~ -exp(2*sqrt(3)*n*Pi) / (2^(5/2)*Pi*n^2). - _Vaclav Kotesovec_, Feb 20 2018
%t CoefficientList[Series[(2 * QPochhammer[-1, x])^2 / (65536 + x*QPochhammer[-1, x]^24)^(1/4), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 20 2018 *)
%Y (q*j(q))^(k/24): A289397 (k=-1), this sequence (k=-2), A299827 (k=-3), A299828 (k=-4), A299829 (k=-5), A299830 (k=-6), A299831 (k=-8), A299832 (k=-12).
%Y Cf. A000521, A289297.
%K sign
%O 0,2
%A _Seiichi Manyama_, Feb 20 2018
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