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A058497
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McKay-Thompson series of class 14A for Monster.
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2
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1, 0, 11, 20, 57, 92, 207, 312, 623, 932, 1674, 2464, 4162, 6024, 9595, 13748, 21126, 29820, 44449, 62004, 90191, 124288, 177135, 241632, 338508, 457272, 631031, 845008, 1150752, 1528380, 2057700, 2712192, 3614217, 4730148, 6245541, 8119672
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OFFSET
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-1,3
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LINKS
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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
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FORMULA
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a(n) ~ exp(2*Pi*sqrt(2*n/7)) / (2^(3/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017
Expansion of A - 4 + 1/A, where A = (eta(q^2)*eta(q^7)/(eta(q)*eta(q^14) ))^4, in powers of q. - G. C. Greubel, Jun 18 2018
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EXAMPLE
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T14A = 1/q + 11*q + 20*q^2 + 57*q^3 + 92*q^4 + 207*q^5 + 312*q^6 + 623*q^7 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; e14C := (eta[q^2]*eta[q^7]/(eta[q] *eta[q^14]))^4; a:= CoefficientList[Series[-4 + e14C + 1/e14C, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^7)/(eta(q)*eta(q^14) ))^4/q; Vec(A - 4 + 1/A) \\ G. C. Greubel, Jun 18 2018
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Cf. A134782 (same sequence except for n=0).
Sequence in context: A158245 A076851 A164576 * A134782 A067969 A068599
Adjacent sequences: A058494 A058495 A058496 * A058498 A058499 A058500
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Nov 27 2000
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EXTENSIONS
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More terms from Michel Marcus, Feb 19 2014
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STATUS
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approved
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