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%I #25 Jun 29 2018 03:37:22
%S 1,-9,-15,-33,-69,-138,-254,-453,-762,-1271,-2025,-3225,-4980,-7653,
%T -11472,-17124,-25095,-36507,-52481,-74934,-105876,-148643,-206982,
%U -286437,-393488,-537828,-730362,-987110,-1326579,-1775037,-2363135,-3133227,-4135902,-5438789,-7123452,-9296976
%N McKay-Thompson series of class 14a for Monster.
%H G. C. Greubel, <a href="/A058505/b058505.txt">Table of n, a(n) for n = -1..1000</a>
%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Comm. Algebra 22, No. 13, 5175-5193 (1994).
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Expansion of A - 7*q/A, where A = q^(1/2)*(eta(q)/eta(q^7))^2, in powers of q. - _G. C. Greubel_, Jun 20 2018
%F a(n) ~ -exp(2*Pi*sqrt(2*n/7)) / (2^(3/4) * 7^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 29 2018
%e T14a = 1/q - 9*q - 15*q^3 - 33*q^5 - 69*q^7 - 138*q^9 - 254*q^11 - ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]/eta[q^7])^2; a:= CoefficientList[Series[A - 7*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* _G. C. Greubel_, Jun 20 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q)/eta(q^7))^2; Vec(A - 7*q/A) \\ _G. C. Greubel_, Jun 20 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K sign
%O -1,2
%A _N. J. A. Sloane_, Nov 27 2000
%E Terms a(12) onward added by _G. C. Greubel_, Jun 20 2018
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