%I #14 Jul 02 2018 01:36:50

%S 1,1,1,-1,1,0,2,-1,2,1,3,-1,4,1,4,0,5,1,7,-2,8,1,10,-1,12,2,14,-2,17,

%T 3,21,-3,24,3,28,-4,34,4,39,-4,46,5,53,-4,61,4,71,-6,82,6,94,-7,108,7,

%U 124,-8,142,11,162,-11,185,10,210,-12,238,14,271,-15,306,15,345,-14,390,17,439,-20,494

%N McKay-Thompson series of class 56b for the Monster group.

%H G. C. Greubel, <a href="/A112197/b112197.txt">Table of n, a(n) for n = 0..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 + q/A, where A = q^(1/2)*eta(q^4)*eta(q^14)/(eta(q^2)* eta(q^28)), in powers of q. - _G. C. Greubel_, Jul 01 2018

%e T56b = 1/q + q + q^3 - q^5 + q^7 + 2*q^11 - q^13 + 2*q^15 + q^17 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^4]*eta[q^14]/(eta[q^2]*eta[q^28])); a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jul 01 2018 *)

%o (PARI) q='q+O('q^50); A = eta(q^4)*eta(q^14)/(eta(q^2)*eta(q^28)); Vec(A + q/A) \\ _G. C. Greubel_, Jul 01 2018

%K sign

%O 0,7

%A _Michael Somos_, Aug 28 2005