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A112203
McKay-Thompson series of class 60e for the Monster group.
1
1, 1, 0, 1, -1, 0, 1, 0, 0, 2, -1, 0, 2, 1, 0, 2, 0, 0, 3, 0, 0, 4, -1, 0, 4, 1, 0, 6, -1, 0, 7, 2, 0, 8, -2, 0, 10, 2, 0, 12, -2, 0, 14, 2, 0, 16, -1, 0, 19, 2, 0, 22, -3, 0, 26, 2, 0, 30, -3, 0, 35, 5, 0, 41, -5, 0, 47, 4, 0, 54, -5, 0, 62, 6, 0, 70, -4, 0, 80, 4, 0, 92, -7, 0, 104, 7, 0, 118, -7, 0, 135
OFFSET
0,10
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of A + q/A, where A = q^(1/2)*(eta(q^6)*eta(q^15)/( eta(q^3)* eta(q^30))), in powers of q. - G. C. Greubel, Jun 28 2018
EXAMPLE
T60e = 1/q +q +q^5 -q^7 +q^11 +2*q^17 -q^19 +2*q^23 +q^25 +...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^6]*eta[q^15]/( eta[q^3]*eta[q^30])); a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 28 2018 *)
PROG
(PARI) q='q+O('q^50); A = (eta(q^6)*eta(q^15)/(eta(q^3)*eta(q^30))); Vec(A + q/A) \\ G. C. Greubel, Jun 28 2018
CROSSREFS
Sequence in context: A137269 A343348 A112201 * A196279 A132798 A080425
KEYWORD
sign
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved