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A058611 McKay-Thompson series of class 29A for Monster. 3
1, 0, 3, 4, 7, 10, 17, 22, 32, 44, 62, 80, 112, 144, 193, 248, 323, 410, 530, 664, 845, 1054, 1324, 1634, 2037, 2498, 3082, 3760, 4601, 5580, 6789, 8186, 9891, 11876, 14271, 17052, 20393, 24260, 28876, 34224, 40557, 47888, 56540, 66516, 78240 (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

a(n) ~ exp(4*Pi*sqrt(n/29)) / (sqrt(2)*29^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

G.f.: - 2 + x^(-1) * ( G(x) * G(x^29) + x^6 * H(x) * H(x^29) )^2 where G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 18 2018

EXAMPLE

T29A = 1/q + 3*q + 4*q^2 + 7*q^3 + 10*q^4 + 17*q^5 + 22*q^6 + 32*q^7 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; e26B := ((eta[q^2]*eta[q^13])/(eta[q] *eta[q^26]))^2; G[q_] := QPochhammer[q^2, q^5]*QPochhammer[q^3, q^5]* QPochhammer[q^5]/QPochhammer[q]; H[q_] := QPochhammer[q, q^5]* QPochhammer[q^4, q^5]*QPochhammer[q^5]/QPochhammer[q]; a:= CoefficientList[Series[q*(-2 + (1/q)*(G[q]*G[q^29] + q^6*H[q]*H[q^29])^2 ), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

CROSSREFS

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

Cf. A136570 (same sequence except for n=0).

Sequence in context: A147955 A256912 A134591 * A098613 A261037 A280423

Adjacent sequences:  A058608 A058609 A058610 * A058612 A058613 A058614

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 18 2014

STATUS

approved

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Last modified January 20 04:14 EST 2019. Contains 319323 sequences. (Running on oeis4.)