A058544 - OEIS

A058544

McKay-Thompson series of class 18f for the Monster group.

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

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OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500

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 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

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

Sequence in context: A260211 A255008 A222602 * A112156 A285723 A072328

Adjacent sequences: A058541 A058542 A058543 * A058545 A058546 A058547

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved