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%I #15 Mar 06 2018 10:54:24
%S 1,-93,14310,-2598835,504870840,-101820075030,21033065244233,
%T -4418043012449640,939524696045366400,-201695299876429277490,
%U 43625340820210623183729,-9493467131549164702157730,2076344691467486382060290550
%N Coefficients in expansion of (q*j(q))^(-1/8) where j(q) is the elliptic modular invariant (A000521).
%F Convolution inverse of A289298.
%F a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(5/8), where c = 0.433852674132039602551793002786117867365165961976868338756... = 2^(3/8) * exp(sqrt(3) * Pi/8) * Pi^(3/2) / (3^(3/8) * Gamma(1/3)^(9/4) * Gamma(3/8)). - _Vaclav Kotesovec_, Feb 20 2018, updated Mar 06 2018
%F a(n) * A289298(n) ~ -3*2^(1/4)*sqrt(1+sqrt(2)) * exp(2*sqrt(3)*Pi*n) / (16*Pi*n^2). - _Vaclav Kotesovec_, Feb 20 2018
%t CoefficientList[Series[(2 * QPochhammer[-1, x])^3 / (65536 + x*QPochhammer[-1, x]^24)^(3/8), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 20 2018 *)
%Y Cf. A000521, A289298.
%K sign
%O 0,2
%A _Seiichi Manyama_, Feb 20 2018
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