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A058641
McKay-Thompson series of class 35B for Monster.
2
1, 0, 2, 3, 5, 6, 10, 12, 18, 23, 31, 39, 54, 66, 86, 107, 137, 168, 213, 259, 323, 392, 482, 580, 711, 850, 1029, 1228, 1476, 1750, 2093, 2470, 2934, 3453, 4078, 4780, 5625, 6566, 7689, 8952, 10440, 12113, 14080, 16286, 18865, 21764, 25127, 28910, 33289
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 -1 + (eta(q^5)*eta(q^7))/(eta(q)*eta(q^35)) in powers of q. - G. C. Greubel, Jan 28 2018
a(n) ~ exp(4*Pi*sqrt(n/35)) / (sqrt(2) * 35^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018
EXAMPLE
T35B = 1/q + 2*q + 3*q^2 + 5*q^3 + 6*q^4 + 10*q^5 + 12*q^6 + 18*q^7 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[-1 + (eta[q^5]*eta[q^7])/(eta[q]*eta[q^35]), {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Jan 28 2018)
PROG
(PARI) q='q+O('q^50); A = -1 + (eta(q^5)*eta(q^7))/(eta(q)*eta(q^35))/q; Vec(A) \\ G. C. Greubel, Jun 14 2018
CROSSREFS
Cf. A212253 (same sequence except for n=0).
Sequence in context: A347446 A097071 A105420 * A212253 A237831 A347443
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 18 2014
STATUS
approved