A058493 McKay-Thompson series of class 12e for Monster.

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

Offset

0,2

Comments

Agrees with A112149 except for signs.

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

Example

T12e = 1/q + 4*q - 4*q^5 + 16*q^7 + 6*q^11 + 40*q^13 - 8*q^17 + 96*q^19 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; b:= q^(1/2)*(eta[q^3]/eta[q^6])^4;
a:= CoefficientList[Series[b + 4*q/b, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 13 2018 *)

Prog

(PARI) q='q+O('q^60); A = (eta(q^3)/eta(q^6))^4; Vec(A + 4*q/A) \\ G. C. Greubel, Jun 13 2018

Crossrefs

Cf. A000521, A007240, A007263, A014708, A007241, A007267, A045478, A112149, etc.

Sequence in context: A371377 A154854 A151672 * A112149 A087736 A005075

Adjacent sequences: A058490 A058491 A058492 * A058494 A058495 A058496

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Status

approved