A058103 McKay-Thompson series of class 10b for Monster.

1, 0, 2, -4, 7, 12, 0, 4, -13, 12, 32, 0, 27, -44, 60, 104, 0, 44, -94, 104, 219, 0, 136, -244, 300, 532, 0, 240, -479, 520, 1028, 0, 572, -1012, 1206, 2132, 0, 968, -1848, 2028, 3850, 0, 2010, -3560, 4114, 7292, 0, 3320, -6185, 6772, 12554, 0, 6267, -11088

Offset

-1,3

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000 (terms -1..498 from G. A. Edgar)

D. Alexander, C. Cummins, J. McKay and C. Simons, Completely Replicable Functions, LMS Lecture Notes, 165, ed. Liebeck and Saxl (1992), 87-98, annotated and scanned copy.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

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

Example

T10b = 1/q + 2*q - 4*q^2 + 7*q^3 + 12*q^4 + 4*q^6 - 13*q^7 + 12*q^8 + ...

Mathematica

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A277339 A153555 A259588 * A346268 A097592 A267699

Adjacent sequences: A058100 A058101 A058102 * A058104 A058105 A058106

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Status

approved