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A058725 McKay-Thompson series of class 60A for the Monster group. 1
1, 2, 0, 1, 1, 3, 1, 6, 3, 5, 7, 9, 8, 14, 9, 17, 18, 24, 21, 33, 30, 40, 43, 54, 52, 77, 69, 93, 97, 117, 121, 160, 153, 191, 200, 246, 250, 319, 312, 381, 410, 480, 494, 607, 609, 733, 775, 903, 937, 1120, 1152, 1345, 1431, 1638, 1712, 2020, 2085, 2406 (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 + q/A, where A = q^(1/2)*(eta(q^2)*eta(q^3)*eta(q^10) *eta(q^15)/(eta(q)*eta(q^5)*eta(q^6)*eta(q^30))), in powers of q. - G. C. Greubel, Jun 28 2018

a(n) ~ exp(2*Pi*sqrt(n/15)) / (2 * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T60A = 1/q + 2*q + q^5 + q^7 + 3*q^9 + q^11 + 6*q^13 + 3*q^15 + 5*q^17 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^3]* eta[q^10]*eta[q^15]/(eta[q]*eta[q^5]*eta[q^6]*eta[q^30]));  a:= SeriesCoefficient[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 28 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15)/(eta(q)* eta(q^5)*eta(q^6)*eta(q^30))); Vec(A + q/A) \\ G. C. Greubel, Jun 28 2018

CROSSREFS

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

Sequence in context: A029347 A303427 A176076 * A068446 A253830 A167625

Adjacent sequences:  A058722 A058723 A058724 * A058726 A058727 A058728

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved

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Last modified January 20 23:20 EST 2019. Contains 319343 sequences. (Running on oeis4.)