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A112169 McKay-Thompson series of class 28B for the Monster group. 2
1, 0, 3, 4, 9, 12, 15, 24, 39, 52, 66, 96, 130, 168, 219, 292, 390, 492, 625, 804, 1023, 1280, 1599, 2016, 2508, 3096, 3807, 4688, 5760, 7020, 8532, 10368, 12585, 15156, 18213, 21912, 26287, 31404, 37410, 44584, 53004, 62784, 74245, 87768, 103578 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1500

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

Expansion of A + 1 + 4/A, where A = eta(q)*eta(q^7)/(eta(q^4)*eta(q^28)), in powers of q. - G. C. Greubel, Jun 25 2018

a(n) ~ exp(2*Pi*sqrt(n/7)) / (2 * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

EXAMPLE

T28B = 1/q + 3*q + 4*q^2 + 9*q^3 + 12*q^4 + 15*q^5 + 24*q^6 + 39*q^7 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q]*eta[q^7]/(eta[q^4]* eta[q^28])); a:= CoefficientList[Series[q*(1 + A + 4/A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 1502}] (* G. C. Greubel, Jun 25 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q)*eta(q^7)/(q*eta(q^4)*eta(q^28)); Vec(A + 1 + 4/A) \\ G. C. Greubel, Jun 25 2018

CROSSREFS

Sequence in context: A010427 A127163 A058503 * A155564 A105137 A243185

Adjacent sequences:  A112166 A112167 A112168 * A112170 A112171 A112172

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 16 03:15 EST 2019. Contains 319184 sequences. (Running on oeis4.)