A112149 McKay-Thompson series of class 12f for the Monster group.

1, -4, 0, -4, -16, 0, 6, -40, 0, -8, -96, 0, 17, -204, 0, -28, -400, 0, 38, -760, 0, -56, -1376, 0, 84, -2404, 0, -124, -4096, 0, 172, -6808, 0, -232, -11072, 0, 325, -17688, 0, -448, -27792, 0, 594, -43008, 0, -784, -65696, 0, 1049, -99128, 0, -1388, -147888, 0, 1796, -218408, 0, -2320

Offset

0,2

Comments

The convolution square of this sequence is A007263 except for the constant term: T12e(q)^2 = T6d(q^2) - 8. - G. A. Edgar, Apr 17 2017

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

Formula

Expansion of q^(1/2) * (eta(q^3)^4/eta(q^6)^4 - 4*eta(q^6)^4/eta(q^3)^4) in powers of q. - G. A. Edgar, Apr 17 2017

Example

T12f = 1/q -4*q -4*q^5 -16*q^7 +6*q^11 -40*q^13 -8*q^17 +...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/2)* (eta[q^3]^4/eta[q^6]^4 - 4*eta[q^6]^4/eta[q^3]^4), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 25 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^3)/eta(q^6))^4; Vec(A - 4*q/A) \\ G. C. Greubel, Jun 16 2018

Crossrefs

Cf. A007263, A058493, etc.

Sequence in context: A154854 A151672 A058493 * A087736 A005075 A103638

Adjacent sequences: A112146 A112147 A112148 * A112150 A112151 A112152

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved