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A058646
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McKay-Thompson series of class 36C for Monster.
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2
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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EXAMPLE
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T36C = 1/q + q + 3*q^3 + 2*q^5 + 7*q^7 + 6*q^9 + 12*q^11 + 10*q^13 + ...
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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