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 A058646 McKay-Thompson series of class 36C for Monster. 2
 1, 1, 3, 2, 7, 6, 12, 10, 21, 22, 36, 36, 59, 63, 93, 98, 142, 156, 218, 238, 327, 358, 482, 528, 696, 769, 996, 1106, 1411, 1572, 1978, 2206, 2745, 3068, 3776, 4224, 5161, 5778, 6999, 7832, 9429, 10554, 12612, 14112, 16776, 18782, 22190, 24828, 29195, 32666, 38220, 42730, 49794, 55656, 64598, 72146, 83439, 93134, 107346 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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, Commun. Algebra 22, No. 13, 5175-5193 (1994). FORMULA G.f.: (E(q^6)*E(q^12))^2/(E(q^2)*E(q^4)*E(q^18)*E(q^36))/q where E(q) = prod(n>=1, 1 - q^n ), note that every second term is zero and has been omitted from this sequence, cf. the pari/GP program. - Joerg Arndt, Apr 09 2016 a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 10 2015 EXAMPLE T36C = 1/q + q + 3*q^3 + 2*q^5 + 7*q^7 + 6*q^9 + 12*q^11 + 10*q^13 + ... MATHEMATICA nmax = 50; CoefficientList[Series[Product[((1-x^(3*k)) * (1-x^(6*k)))^2 / ((1-x^k) * (1-x^(2*k)) * (1-x^(9*k)) * (1-x^(18*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 10 2015 *) eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q^3]*eta[q^6])^2/(eta[q]*eta[q^2]*eta[q^9]*eta[q^18]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *) PROG (PARI) { N=66; q='q+O('q^N); my(E=eta); Vec( (E(q^3)*E(q^6))^2 / (E(q^1)*E(q^2)*E(q^9)*E(q^18))/q ) } \\ Joerg Arndt, Apr 09 2016 CROSSREFS Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc. Sequence in context: A122336 A122355 A175433 * A323635 A125718 A268821 Adjacent sequences:  A058643 A058644 A058645 * A058647 A058648 A058649 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 27 2000 EXTENSIONS Offset corrected by N. J. A. Sloane, Feb 17 2014 More terms from Vaclav Kotesovec, Sep 10 2015 STATUS approved

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Last modified October 23 19:37 EDT 2019. Contains 328373 sequences. (Running on oeis4.)