cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A112172 McKay-Thompson series of class 32d for the Monster group.

This page as a plain text file.
%I A112172 #17 Jun 16 2018 18:32:23
%S A112172 1,-2,0,0,-1,-2,0,0,-1,-4,0,0,0,-6,0,0,1,-8,0,0,0,-12,0,0,-1,-18,0,0,
%T A112172 1,-24,0,0,2,-32,0,0,-1,-44,0,0,-2,-58,0,0,1,-76,0,0,2,-100,0,0,-1,
%U A112172 -128,0,0,-3,-164,0,0,1,-210,0,0,4,-264,0,0,-2,-332,0,0,-5,-416,0,0,2,-516,0,0,5,-640,0,0,-2,-790,0,0
%N A112172 McKay-Thompson series of class 32d for the Monster group.
%H A112172 G. C. Greubel, <a href="/A112172/b112172.txt">Table of n, a(n) for n = 0..5000</a>
%H A112172 D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).
%H A112172 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F A112172 Expansion of A - 2*q/A, where A = q^(1/2)*eta(q^4)/eta(q^16), in powers of q. - _G. C. Greubel_, Jun 16 2018
%e A112172 T32d = 1/q - 2*q - q^7 - 2*q^9 - q^15 - 4*q^17 - 6*q^25 + q^31 + ...
%t A112172 QP = QPochhammer; G[q_]:= QP[q^2, q^5]*QP[q^3, q^5]*QP[q^5, q^5]/QP[q, q]; H[q_]:= QP[q, q^5]*QP[q^4, q^5]*QP[q^5, q^5]/QP[q, q]; a[n_]:= SeriesCoefficient[(G[q]*G[q^19] + q^4*H[q]*H[q^19])^3/q - 3, {q,0,n}]; Table[A058549[n], {n,-1,50}] (* _G. C. Greubel_, Feb 18 2018 *)
%t A112172 eta[q_]:= q^(1/24)*QPochhammer[q]; A := q^(1/2)*eta[q^4]/eta[q^16]; a:=
%t A112172 CoefficientList[Series[(A - 2*q/A), {q, 0, 100}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 16 2018 *)
%o A112172 (PARI) q='q+O('q^50); A = eta(q^4)/eta(q^16); Vec(A - 2*q/A) \\ _G. C. Greubel_, Jun 16 2018
%K A112172 sign
%O A112172 0,2
%A A112172 _Michael Somos_, Aug 28 2005