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%I #13 Mar 06 2018 10:52:50
%S 1,-124,21002,-4016872,809288755,-167876361244,35484423032510,
%T -7599636959859112,1643483711343623769,-358082233874320665600,
%U 78482787856608918842534,-17284562763499415545585456,3821876235203430873578026310
%N Coefficients in expansion of (q*j(q))^(-1/6) where j(q) is the elliptic modular invariant (A000521).
%F Convolution inverse of A289299.
%F a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / sqrt(n), where c = 0.585669299547026632252908661746743778408088234535945502931... = sqrt(2) * exp(Pi/(2 * sqrt(3))) * Pi^(3/2) / (sqrt(3) * Gamma(1/3)^3). - _Vaclav Kotesovec_, Feb 20 2018, updated Mar 06 2018
%F a(n) * A289299(n) ~ -exp(2*sqrt(3)*Pi*n) / (2*Pi*n^2). - _Vaclav Kotesovec_, Feb 20 2018
%t CoefficientList[Series[(2 * QPochhammer[-1, x])^4 / (65536 + x*QPochhammer[-1, x]^24)^(1/2), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 20 2018 *)
%Y Cf. A000521, A289299.
%K sign
%O 0,2
%A _Seiichi Manyama_, Feb 20 2018