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A058544 McKay-Thompson series of class 18f for the Monster group. 1
1, -3, 0, -2, -6, 0, -1, -15, 0, 4, -24, 0, -3, -48, 0, 0, -78, 0, 7, -132, 0, -8, -204, 0, -3, -324, 0, 14, -486, 0, -14, -735, 0, -4, -1068, 0, 26, -1563, 0, -26, -2220, 0, -7, -3159, 0, 44, -4404, 0, -41, -6135, 0, -10, -8412, 0, 73, -11508, 0, -72, -15552, 0, -20, -20964, 0, 118, -27978, 0, -109 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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 - 3*q/A, where q^(1/2)*(eta(q^3)/eta(q^9))^2, in powers of q. - G. C. Greubel, Jun 21 2018
EXAMPLE
T18f = 1/q - 3*q - 2*q^5 - 6*q^7 - q^11 - 15*q^13 + 4*q^17 - 24*q^19 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]/eta[q^9])^2; a:= CoefficientList[Series[A - 3*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)
PROG
(PARI) q='q+O('q^60); A = (eta(q^3)/eta(q^9))^2; Vec(A - 3*q/A) \\ G. C. Greubel, Jun 21 2018
CROSSREFS
Sequence in context: A260211 A255008 A222602 * A112156 A285723 A072328
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)