A112145 McKay-Thompson series of class 8c for the Monster group.

1, -8, -6, -48, 15, -168, -26, -496, 51, -1296, -102, -3072, 172, -6840, -276, -14448, 453, -29184, -728, -56880, 1128, -107472, -1698, -197616, 2539, -354888, -3780, -624048, 5505, -1076736, -7882, -1826416, 11238, -3050400, -15918, -5022720, 22259, -8163152, -30810

Offset: 0

Author

Michael Somos, Aug 28 2005

Keywords

• sign

Comments

This sequence agrees with A058088 except for alternating signs: T8c(q) = i*T8b(i*q). - G. A. Edgar, Mar 25 2017

Examples

			T8c = 1/q -8*q -6*q^3 -48*q^5 +15*q^7 -168*q^9 -26*q^11 +...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..503 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

Crossrefs

Cf. A058088.

Programs

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/2)*(eta[q^4]^8*eta[q]^4/(eta[q^2]^8*eta[q^8]^4) - 4*eta[q^2]^8 *eta[q^8]^4 /(eta[q]^4*eta[q^4]^8)), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 23 2018 *)

PARI

q='q+O('q^30); F= eta(q^4)^8*eta(q)^4/(eta(q^2)^8*eta(q^8)^4) - 4*q*eta(q^2)^8*eta(q^8)^4/(eta(q)^4* eta(q^4)^8); Vec(F) \\ G. C. Greubel, Jun 06 2018

Formula

Expansion of q^(1/2)*(eta(q^4)^8*eta(q)^4 / (eta(q^2)^8*eta(q^8)^4) - 4*eta(q^2)^8*eta(q^8)^4 / (eta(q)^4*eta(q^4)^8)) in powers of q. - G. A. Edgar, Mar 25 2017