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 A058684 McKay-Thompson series of class 45A for Monster. 2
 1, 0, 2, 1, 3, 4, 5, 6, 7, 11, 15, 17, 22, 24, 34, 40, 48, 56, 69, 84, 104, 118, 144, 164, 200, 234, 273, 318, 372, 436, 511, 582, 681, 775, 906, 1036, 1192, 1362, 1562, 1784, 2046, 2315, 2647, 2988, 3409, 3860, 4371, 4936, 5573, 6288, 7104, 7967, 8979, 10052 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,3 LINKS 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). FORMULA Expansion of -1 + (eta(q^3)*eta(q^15))^2/(eta(q)*eta(q^5)*eta(q^9)* eta(q^45)) in powers of q. - G. C. Greubel, Jun 19 2018 a(n) ~ exp(4*Pi*sqrt(n/5)/3) / (5^(1/4) * sqrt(6) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018 EXAMPLE T45A = 1/q + 2*q + q^2 + 3*q^3 + 4*q^4 + 5*q^5 + 6*q^6 + 7*q^7 + 11*q^8 + ... MATHEMATICA eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^3]*eta[q^15])^2/(eta[q] *eta[q^5]*eta[q^9]*eta[q^45]); a:= CoefficientList[Series[-1 + e45A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *) PROG (PARI) q='q+O('q^50); A = -1 + (eta(q^3)*eta(q^15))^2/(eta(q)*eta(q^5) *eta(q^9)*eta(q^45))/q; Vec(A) \\ G. C. Greubel, Jun 19 2018 CROSSREFS Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc. Cf. A226054 (same sequence except for n=0). Sequence in context: A155963 A273863 A273864 * A226054 A109920 A109919 Adjacent sequences:  A058681 A058682 A058683 * A058685 A058686 A058687 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 27 2000 EXTENSIONS More terms from Michel Marcus, Feb 18 2014 STATUS approved

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Last modified April 11 22:01 EDT 2021. Contains 342888 sequences. (Running on oeis4.)