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A058744 McKay-Thompson series of class 70A for Monster. 2
1, 0, 1, 0, 2, 2, 2, 2, 3, 2, 4, 4, 7, 4, 10, 8, 11, 10, 14, 14, 21, 18, 25, 22, 33, 32, 41, 38, 52, 50, 65, 62, 82, 78, 101, 102, 124, 122, 150, 152, 189, 186, 230, 226, 279, 280, 334, 340, 402, 412, 487, 492, 582, 592, 697, 714, 831, 850, 980, 1014, 1173 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,5
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum
FORMULA
Expansion of B + 1 + 1/B, where B = eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/ (eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)), in powers of q. - G. C. Greubel, Jun 30 2018
a(n) ~ exp(2*Pi*sqrt(2*n/35)) / (2^(3/4) * 35^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 30 2018
EXAMPLE
T70A = 1/q + q + 2*q^3 + 2*q^4 + 2*q^5 + 2*q^6 + 3*q^7 + 2*q^8 + 4*q^9 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; B:= eta[q]*eta[q^10]*eta[q^14]* eta[q^35]/(eta[q^2]*eta[q^5]*eta[q^7]*eta[q^70]); a:= CoefficientList[ Series[1 + B + 1/B, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 30 2018 *)
PROG
(PARI) q='q+O('q^50); B = eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/ (q*eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)); Vec(B + 1 + 1/B) \\ G. C. Greubel, Jun 30 2018
CROSSREFS
Sequence in context: A029348 A070093 A174931 * A366297 A323246 A364721
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 24 2014
STATUS
approved

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Last modified April 22 17:34 EDT 2024. Contains 371905 sequences. (Running on oeis4.)