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A058599
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McKay-Thompson series of class 27A for the Monster group.
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1
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1, 0, 3, 5, 9, 12, 20, 27, 42, 57, 81, 108, 150, 198, 267, 346, 459, 588, 765, 972, 1248, 1570, 1989, 2484, 3117, 3861, 4800, 5908, 7290, 8916, 10922, 13284, 16170, 19565, 23679, 28512, 34331, 41148, 49308, 58854, 70218, 83484, 99193, 117504, 139092
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OFFSET
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-1,3
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COMMENTS
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Also McKay-Thompson series of class 27B for the Monster group.
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = -1..10000 (terms -1..1000 from G. C. Greubel)
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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Expansion of T9B(q)/(1 - 3*T9B(q)/(6 + T9B(q^3))), where T9B(q) = A058091 and T9B(q^3) = T9B(q -> q^3), in powers of q. - G. C. Greubel, Jun 22 2018
a(n) ~ exp(4*Pi*sqrt(n/3)/3) / (sqrt(2) * 3^(3/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
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EXAMPLE
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T27A = 1/q +3*q +5*q^2 +9*q^3 +12*q^4 +20*q^5 +27*q^6 +42*q^7 +...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; nmax := 100; B:= (eta[q^6]/eta[q^3])*(eta[q^9]/eta[q^18])^3; T9B := B + 4/(B)^2; A:= T9B/(6 + (T9B/.{q -> q^3})) ; a:= CoefficientList[Series[q*T9B/(1 - 3*A + O[q]^nmax), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 22 2018 *)
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PROG
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(PARI) q='q+O('q^50); B = (eta(q^6)/eta(q^3))*(eta(q^9)/eta(q^18))^3/q; B3 = (eta(q^18)/eta(q^9))*(eta(q^27)/eta(q^54))^3/q^3; T9B = B + 4/B^2; T9B3 = B3 + 4/(B3)^2; A = T9B/(6 + T9B3); Vec(T9B/(1 - 3*A)) \\ G. C. Greubel, Jun 22 2018
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Sequence in context: A190310 A046746 A344715 * A238662 A059093 A084593
Adjacent sequences: A058596 A058597 A058598 * A058600 A058601 A058602
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Nov 27 2000
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STATUS
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approved
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