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A112195 McKay-Thompson series of class 54d for the Monster group. 1
1, 1, -1, 1, 0, 0, 1, 1, 0, 2, 1, -1, 2, 1, -1, 2, 1, -1, 4, 3, -2, 4, 2, -1, 5, 3, -2, 7, 4, -3, 8, 4, -3, 9, 5, -3, 13, 8, -6, 14, 7, -5, 16, 10, -6, 21, 12, -9, 24, 13, -9, 27, 15, -10, 35, 21, -15, 39, 20, -14, 45, 26, -17, 55, 31, -22, 62, 34, -23, 70, 39, -26, 86, 50, -35, 96, 51, -35, 109, 62, -41, 130 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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(T27d) in powers of q, where T27d = A058604. - G. C. Greubel, Jul 01 2018

EXAMPLE

T54d = 1/q + q^5 - q^11 + q^17 + q^35 + q^41 + 2*q^53 + q^59 - q^65 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax := 100; A:= q*(eta[q^3]/ eta[q^9])^4; T9b := (A + 9*q^2/A); T27d := (6*q + T9b + O[q]^nmax)^(1/3); a:= CoefficientList[Series[(T27d + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)

PROG

(PARI) q='q+O('q^80); A = (eta(q^3)/eta(q^9))^4; T9b = A + 9*q^2/A; T27d = (6*q + T9b)^(1/3); Vec(sqrt(T27d)) \\ G. C. Greubel, Jul 01 2018

CROSSREFS

Sequence in context: A152828 A233285 A233284 * A103956 A103957 A232550

Adjacent sequences:  A112192 A112193 A112194 * A112196 A112197 A112198

KEYWORD

sign

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 16 03:30 EST 2019. Contains 319184 sequences. (Running on oeis4.)