A058204 McKay-Thompson series of class 10c for Monster.

1, -2, -5, 0, -5, 8, -9, -20, 0, -10, 23, -32, -60, 0, -35, 68, -76, -150, 0, -80, 154, -186, -350, 0, -185, 342, -393, -740, 0, -370, 698, -808, -1495, 0, -755, 1380, -1559, -2870, 0, -1400, 2576, -2926, -5335, 0, -2595, 4710, -5270, -9580, 0, -4580, 8304, -9304, -16790, 0, -7985, 14360, -15947

Offset

0,2

Comments

The convolution square of this sequence is A007253 except for the constant term: T10c(q)^2 + 4 = T5a(q^2). - G. A. Edgar, Apr 03 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..499 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, Vol. 22, No. 13 (1994), 5175-5193.

Index entries for McKay-Thompson series for Monster simple group

Example

T10c = 1/q - 2*q - 5*q^3 - 5*q^7 + 8*q^9 - 9*q^11 - 20*q^13 - 10*q^17 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 110; e25a:= eta[q]/eta[q^25];
e5B := (eta[q]/eta[q^5])^6; T5a := (1 + 5/e25a)*(1 + e5B) + 5*(e25a - 5/e25a)*(e5B/(e25a)^3); a:= CoefficientList[Series[((q (T5a - 4) + O[q]^nmax // Normal /. {q -> q^2}) + O[q]^nmax)^(1/2) // Normal, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

Crossrefs

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

Sequence in context: A024714 A123342 A196816 * A242969 A268886 A090625

Adjacent sequences: A058201 A058202 A058203 * A058205 A058206 A058207

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Status

approved