%I #22 Jun 29 2018 03:39:26
%S 1,-6,-7,-14,-20,-42,-55,-112,-139,-252,-314,-524,-678,-1042,-1335,
%T -1980,-2553,-3688,-4681,-6592,-8341,-11520,-14557,-19626,-24692,
%U -32834,-41135,-54016,-67279,-87328,-108285,-139176,-171984,-218808,-269296,-339844,-416715,-522236,-637642,-793736
%N McKay-Thompson series of class 20a for Monster.
%H G. C. Greubel, <a href="/A058556/b058556.txt">Table of n, a(n) for n = -1..2500</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 -4*q/A, where A = q(1/2)*(eta(q)*eta(q^5)/(eta(q^2) *eta(q^10)))^2, in powers of q. - _G. C. Greubel_, Jun 21 2018
%F a(n) ~ -exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 29 2018
%e T20a = 1/q - 6*q - 7*q^3 - 14*q^5 - 20*q^7 - 42*q^9 - 55*q^11 - 112*q^13 - ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q]*eta[q^5]/(eta[q^2]*eta[q^10]))^2; a:= CoefficientList[Series[A - 4*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 21 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q)*eta(q^5)/(eta(q^2) *eta(q^10)))^2; Vec(A - 4*q/A) \\ _G. C. Greubel_, Jun 21 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 21 2018