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A058566 McKay-Thompson series of class 21D for Monster. 2
1, 0, 5, 8, 16, 26, 44, 66, 104, 152, 229, 324, 469, 652, 916, 1250, 1716, 2306, 3108, 4116, 5464, 7156, 9373, 12144, 15725, 20190, 25889, 32952, 41881, 52904, 66716, 83688, 104785, 130608, 162486, 201336, 249006, 306874, 377482, 462860, 566513, 691404 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,3
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of -2 + (eta(q^3)*eta(q^7)/(eta(q)*eta(q^21)))^2 in powers of q. - G. C. Greubel, Jun 14 2018
a(n) ~ exp(4*Pi*sqrt(n/21)) / (sqrt(2) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
EXAMPLE
T21D = 1/q + 5*q + 8*q^2 + 16*q^3 + 26*q^4 + 44*q^5 + 66*q^6 + 104*q^7 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-2 + (eta[q^3]*eta[q^7]/(eta[q]*eta[q^21]))^2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)
PROG
(PARI) q='q+O('q^50); A = -2+(eta(q^3)*eta(q^7)/(eta(q)*eta(q^21)))^2/q; Vec(A) \\ G. C. Greubel, Jun 14 2018
CROSSREFS
Cf. A226015 (same sequence except for n=0).
Sequence in context: A073136 A063924 A340997 * A153363 A154119 A196387
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 February 24 05:36 EST 2024. Contains 370291 sequences. (Running on oeis4.)