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A112156 McKay-Thompson series of class 18g 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

G. C. Greubel, Table of n, a(n) for n = 0..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of A + 3*q/A, where A = q^(1/2)*(eta(q^3)/eta(q^9))^2, in powers of q. - G. C. Greubel, Jun 25 2018

EXAMPLE

T18g = 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 25 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^3)/eta(q^9))^2; Vec(A + 3*q/A) \\ G. C. Greubel, Jun 25 2018

CROSSREFS

Sequence in context: A255008 A222602 A058544 * A285723 A072328 A135040

Adjacent sequences:  A112153 A112154 A112155 * A112157 A112158 A112159

KEYWORD

sign

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 21 19:54 EST 2019. Contains 319350 sequences. (Running on oeis4.)