login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

McKay-Thompson series of class 56b for the Monster group.
1

%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