A058546 - OEIS

%I #14 Jun 21 2018 21:21:26

%S 1,0,4,-2,0,8,1,0,12,-4,0,32,8,0,52,-6,0,80,10,0,148,-16,0,224,18,0,

%T 332,-26,0,536,33,0,784,-40,0,1120,58,0,1676,-74,0,2368,82,0,3296,

%U -112,0,4704,147,0,6472,-166,0,8808,212,0,12160,-268,0,16384,316,0,21884,-392,0,29472,476

%N McKay-Thompson series of class 18h for Monster.

%H G. C. Greubel, <a href="/A058546/b058546.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^2/A, where A = q*(eta(q^3)*eta(q^9)/(eta(q^6) *eta(q^18)))^2, in powers of q. - _G. C. Greubel_, Jun 21 2018

%e T18h = 1/q + 4*q - 2*q^2 + 8*q^4 + q^5 + 12*q^7 - 4*q^8 + 32*q^10 + 8*q^11 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q*(eta[q^3]*eta[q^9]/(eta[q^6] *eta[q^18]))^2; a:= CoefficientList[Series[A + 4*q^2/A, {q, 0, 80}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 21 2018 *)

%o (PARI) q='q+O('q^60); A = (eta(q^3)*eta(q^9)/(eta(q^6)*eta(q^18)))^2; Vec(A + 4*q^2/A) \\ _G. C. Greubel_, Jun 21 2018

%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

%K sign

%O -1,3

%A _N. J. A. Sloane_, Nov 27 2000

%E Terms a(24) onward added by _G. C. Greubel_, Jun 21 2018