|
%I #28 Jul 25 2022 22:40:30
%S 1,0,2,-4,7,12,0,4,-13,12,32,0,27,-44,60,104,0,44,-94,104,219,0,136,
%T -244,300,532,0,240,-479,520,1028,0,572,-1012,1206,2132,0,968,-1848,
%U 2028,3850,0,2010,-3560,4114,7292,0,3320,-6185,6772,12554,0,6267,-11088
%N McKay-Thompson series of class 10b for Monster.
%H G. C. Greubel, <a href="/A058103/b058103.txt">Table of n, a(n) for n = -1..1000</a> (terms -1..498 from G. A. Edgar)
%H D. Alexander, C. Cummins, J. McKay and C. Simons, <a href="http://oeis.org/A007242/a007242_1.pdf">Completely Replicable Functions</a>, LMS Lecture Notes, 165, ed. Liebeck and Saxl (1992), 87-98, annotated and scanned copy.
%H 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 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F The g.f. T10b satisfies the quintic equation P5(T10b(q)) = T2A(q^5), where we used T2A from A101558 and polynomial P5(t) = t^5-10*t^3+20*t^2-15*t-100. - _G. A. Edgar_, Apr 03 2017
%e T10b = 1/q + 2*q - 4*q^2 + 7*q^3 + 12*q^4 + 4*q^6 - 13*q^7 + 12*q^8 + ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= eta[q]/eta[q^25]; B:= (eta[q^2]* eta[q^25])/(eta[q]*eta[q^50]); c:= ((eta[q]*eta[q^2])/(eta[q^5]* eta[q^10]))^2; f5:= (c/. {q -> q^5}); a:= CoefficientList[Series[ Simplify[ q*(2 + c + 5*(c/(A)^2)*(1 - 1/B)^2 + 25/f5), q>0], {q,0,60}], q]; Table[ a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 17 2018, fixed by _Vaclav Kotesovec_, Jul 03 2018 *)
%o (PARI) q='q+O('q^50); A= eta(q)/(q*eta(q^25)); B = (eta(q^2)*eta(q^25) )/(q*eta(q)*eta(q^50)); C=((eta(q)*eta(q^2))/(eta(q^5)*eta(q^10)))^2/q; f5=((eta(q^5)*eta(q^10))/(eta(q^25)*eta(q^50)))^2/q^5; Vec(2 + C + 5*(C/(A)^2)*(1 - 1/B)^2 + 25/f5) \\ _G. C. Greubel_, Jun 17 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K sign
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
|
