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 A112209 McKay-Thompson series of class 80a for the Monster group. 2
 1, 1, 0, 1, 1, 2, 2, 1, 3, 3, 3, 3, 4, 5, 5, 7, 8, 8, 9, 10, 13, 15, 14, 17, 20, 23, 24, 26, 31, 34, 38, 41, 46, 52, 55, 62, 70, 75, 82, 90, 103, 112, 118, 131, 145, 161, 172, 185, 208, 225, 244, 265, 288, 316, 339, 370, 404, 435, 469, 507, 557, 601, 640, 696, 755, 818 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994). FORMULA a(n) ~ exp(Pi*sqrt(n/5)) / (2^(3/2) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 30 2017 Expansion of q^(1/4)*(eta(q^2)*eta(q^10))^2/( eta(q)*eta(q^4)*eta(q^5) *eta(q^20)) in powers of q. - G. C. Greubel, Jun 20 2018 EXAMPLE T80a = 1/q +q^3 +q^11 +q^15 +2*q^19 +2*q^23 +q^27 +3*q^31 +... MATHEMATICA nmax = 70; CoefficientList[Series[Product[(1 + x^(2*k-1))/((1 + x^(10*k))*(1 - x^(10*k-5))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 30 2017 *) eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/4)*(eta[q^2]*eta[q^10])^2/( eta[q]*eta[q^4]*eta[q^5]*eta[q^20]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 70}] (* G. C. Greubel, Jun 20 2018 *) PROG (PARI) q='q+O('q^70); Vec((eta(q^2)*eta(q^10))^2/( eta(q)*eta(q^4) *eta(q^5)*eta(q^20))) \\ G. C. Greubel, Jun 20 2018 CROSSREFS Cf. A112182. Sequence in context: A091224 A308684 A112182 * A240127 A109524 A191521 Adjacent sequences:  A112206 A112207 A112208 * A112210 A112211 A112212 KEYWORD nonn AUTHOR Michael Somos, Aug 28 2005 STATUS approved

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Last modified June 2 12:24 EDT 2020. Contains 334771 sequences. (Running on oeis4.)