A058088 McKay-Thompson series of class 8b for Monster.

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, 13108224, 42438, 20814792, -58110

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000 (terms 0..999 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

Expansion of q^(1/2)*(eta(q^2)^4*eta(q^4)^4 / (eta(q)^4*eta(q^8)^4) + 4*eta(q)^4*eta(q^8)^4 / (eta(q^2)^4*eta(q^4)^4)) in powers of q. - G. A. Edgar, Mar 23 2017

Example

T8b = 1/q + 8*q - 6*q^3 + 48*q^5 + 15*q^7 + 168*q^9 - 26*q^11 + 496*q^13 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; F:= (eta[q^2]*eta[q^4]/(eta[q] *eta[q^8]))^4;  a:= CoefficientList[Series[q^(1/2)*(F + 4/F), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 03 2018 *)

Prog

q='q+O('q^30); F= (eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^4; Vec(F + 4*q/F) \\ G. C. Greubel, Jun 03 2018

Crossrefs

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

Agrees with A112145 except for signs.

Sequence in context: A217479 A301495 A112145 * A248291 A038284 A264587

Adjacent sequences: A058085 A058086 A058087 * A058089 A058090 A058091

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from G. A. Edgar, Mar 23 2017

Status

approved