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URL: https://oeis.org/A058707

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A058707
McKay-Thompson series of class 52a for Monster.
1
1, 2, 0, 2, 1, 4, 3, 6, 5, 10, 8, 14, 13, 20, 19, 28, 26, 40, 39, 54, 54, 76, 75, 100, 103, 136, 138, 180, 183, 236, 245, 308, 320, 402, 417, 516, 541, 664, 696, 844, 890, 1070, 1131, 1350, 1431, 1700, 1802, 2124, 2261, 2648, 2821, 3288, 3507, 4070, 4343, 5014, 5361, 6168, 6593, 7552, 8087
OFFSET
-1,2
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of A + q/A, where A = q^(1/2)*(eta(q^2)*eta(q^13)/(eta(q)* eta(q^26))), in powers of q. - G. C. Greubel, Jun 27 2018
a(n) ~ exp(2*Pi*sqrt(n/13)) / (2 * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
EXAMPLE
T52a = 1/q + 2*q + 2*q^5 + q^7 + 4*q^9 + 3*q^11 + 6*q^13 + 5*q^15 + 10*q^17 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^13]/( eta[q]*eta[q^26])); a:= SeriesCoefficient[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 27 2018 *)
PROG
(PARI) q='q+O('q^50); A = eta(q^2)*eta(q^13)/(eta(q)*eta(q^26)); Vec(A + q/A) \\ G. C. Greubel, Jun 27 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
Terms a(12) onward added by G. C. Greubel, Jun 27 2018
STATUS
approved