A112202 - OEIS

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A112202

McKay-Thompson series of class 60d for the Monster group.

1, -1, -1, 0, 0, 0, 0, -1, 0, -1, 0, -1, -1, 0, 0, 1, 0, -1, 0, -1, 1, -1, -2, 0, -1, 1, -1, -1, 0, -1, 2, -2, -3, 0, 0, 1, -1, -3, 0, -2, 2, -3, -4, 0, -1, 3, -2, -4, 0, -2, 3, -4, -6, 0, -2, 3, -3, -5, 0, -3, 6, -6, -9, 0, -2, 4, -4, -9, 0, -5, 6, -8, -11, 0, -3, 8, -6, -12, 0, -6, 9, -10, -16, 0, -6, 9, -9, -15, 0, -8, 14, -15, -22, 0, -6, 12, -11

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,23

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 sqrt((-8 - T15b(q) - T15b(q^2) + T15b(q)*T15b(q^2))/(5 + T15b(q) + T15b(q^2))) in powers of q, where T15b(q) = A058513. - G. C. Greubel, Jul 02 2018

EXAMPLE

T60d = 1/q -q -q^3 -q^13 -q^17 -q^21 -q^23 +q^29 -q^33 -q^37 +...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= (eta[q]/eta[q^25]); d:= q*(eta[q^3]/eta[q^15])^2; c:= (eta[q^3]*eta[q^5]/(eta[q]* eta[q^15]))^3; T25A := B + 5/B; A:= (eta[q^3]/eta[q^75]); T15b:= Simplify[2 + (-5 + T25A*(A + 5/A))*(-B + A)*(1/(A*B))^2*(d^3/c)/q^3, q>0]; T60d:= CoefficientList[Series[(q*((-8 - T15b - (T15b /. {q -> q^2}) + T15b*(T15b /. {q -> q^2}))/(5 + T15b + (T15b /. {q -> q^2}))) + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[T60d[[n]], {n, 1, nmax}] (* G. C. Greubel, Jul 02 2018 *)

CROSSREFS

Sequence in context: A233323 A115381 A115382 * A126205 A025913 A123230

Adjacent sequences: A112199 A112200 A112201 * A112203 A112204 A112205

KEYWORD

sign

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved