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A112158 McKay-Thompson series of class 20A for the Monster group. 5
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
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
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: A032411 A345034 A058098 * A270046 A093479 A239396
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved

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Last modified March 18 21:02 EDT 2024. Contains 370951 sequences. (Running on oeis4.)