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A058100 McKay-Thompson series of class 10D for the Monster group. 2
1, 0, 21, 62, 162, 378, 819, 1680, 3276, 6138, 11145, 19662, 33840, 57048, 94362, 153432, 245757, 388218, 605466, 933414, 1423614, 2149586, 3215844, 4769544, 7016572, 10243896, 14848809, 21378276, 30582360, 43484304, 61473438, 86428896 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

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

Index entries for McKay-Thompson series for Monster simple group

FORMULA

G.f. is Fourier series of a weight 0 level 10 modular form. f(-1/ ( 10 t)) = f(t) where q = exp(2 Pi i t).

Expansion of -6 + ((eta(q^2)*eta(q^5))/(eta(q)*eta(q^10)))^6 in powers of q. - G. C. Greubel, May 05 2018

a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (2^(3/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T10D = 1/q + 21*q + 62*q^2 + 162*q^3 + 378*q^4 + 819*q^5 + 1680*q^6 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[-6 + ((eta[q^2]*eta[q^5])/(eta[q]*eta[q^10]))^6, {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, May 05 2018 *)

PROG

(PARI) q='q+O('q^30); Vec(-6 + ((eta(q^2)*eta(q^5))/(eta(q)* eta(q^10)) )^6/q) \\ G. C. Greubel, May 05 2018

CROSSREFS

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

Cf. A132130(n) = a(n) unless n=0.

Sequence in context: A126375 A146468 A081302 * A219856 A195106 A143203

Adjacent sequences: A058097 A058098 A058099 * A058101 A058102 A058103

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 19 2014

STATUS

approved

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Last modified November 28 22:51 EST 2022. Contains 358421 sequences. (Running on oeis4.)