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A058493
McKay-Thompson series of class 12e for Monster.
2
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).
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
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
STATUS
approved