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A112158 McKay-Thompson series of class 20A for the Monster group. 4
1, 0, 6, 8, 17, 32, 54, 80, 116, 192, 290, 408, 585, 832, 1192, 1648, 2237, 3072, 4156, 5576, 7414, 9824, 12964, 16896, 22002, 28544, 36794, 47184, 60185, 76736, 97388, 122864, 154615, 194048, 242904, 302800, 376271, 466720, 577176, 711840 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1001

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

a(n) ~ exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 30 2017

Expansion of -4 + ((eta(q^2)*eta(q^10))^2/(eta(q)*eta(q^4)*eta(q^5)* eta(q^20)))^4 in powers of q. - G. C. Greubel, Jun 06 2018

EXAMPLE

T20A = 1/q +6*q +8*q^2 +17*q^3 +32*q^4 +54*q^5 +80*q^6 +...

MATHEMATICA

nmax = 60; Flatten[{1, 0, Rest[Rest[CoefficientList[Series[Product[((1 + x^(2*k-1))/((1 + x^(10*k))*(1 - x^(10*k-5))))^4, {k, 1, nmax}], {x, 0, nmax}], x]]]}] (* Vaclav Kotesovec, Apr 30 2017 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= ((eta[q^2]*eta[q^10])^2/(eta[q] *eta[q^4]*eta[q^5]*eta[q^20]))^4; a:= CoefficientList[Series[q*(-4 + A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 06 2018 *)

PROG

(PARI) q='q+O('q^30); F = ((eta(q^2)*eta(q^10))^2/(eta(q)*eta(q^4)* eta(q^5)*eta(q^20)))^4/q; Vec(-4 + F) \\ G. C. Greubel, Jun 06 2018

CROSSREFS

Sequence in context: A162951 A032411 A058098 * A270046 A093479 A239396

Adjacent sequences:  A112155 A112156 A112157 * A112159 A112160 A112161

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 18 04:47 EST 2019. Contains 319269 sequences. (Running on oeis4.)