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A058513
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McKay-Thompson series of class 15b for Monster.
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5
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1, 0, 3, 2, -3, 0, 0, 6, 6, -8, 6, 0, 16, 12, -9, 10, 0, 36, 21, -30, 18, 0, 63, 48, -53, 36, 0, 114, 78, -84, 67, 0, 210, 140, -159, 96, 0, 336, 237, -266, 183, 0, 553, 378, -396, 284, 0, 900, 595, -672, 435, 0, 1383, 948, -1031, 690, 0, 2116, 1419, -1524, 1062, 0, 3240, 2150, -2349, 1524
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OFFSET
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-1,3
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LINKS
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FORMULA
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Expansion of T15b = 2 + (-5 + T25A*(B + 5/B))*(-A + B)*(1/( B*A))^2*(D^3/C)/q^3 in powers of q, where A = eta(q)/eta(q^25), B = eta(q^3)/ eta(q^75), C = (eta(q^3)*eta(q^5)/(eta(q)*eta(q^15)))^3, D = q*(eta(q^3) /eta(q^15))^2, and T25A = A + 5/A. - G. C. Greubel, Jun 21 2018
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EXAMPLE
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T15b = 1/q + 3*q + 2*q^2 - 3*q^3 + 6*q^6 + 6*q^7 - 8*q^8 + 6*q^9 + 16*q^11 + ...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; nmax=66; A := (eta[q]/eta[q^25]); B := (eta[q^3]/eta[q^75]); c := (eta[q^3]*eta[q^5]/(eta[q]*eta[q^15]))^3; d := q*(eta[q^3]/eta[q^15])^2; T25A := A + 5/A; T15b := 2 + (-5 + T25A*(B + 5/B))*(-A + B)*(1/(B*A))^2*(d^3/c)/q^3; a:= CoefficientList[Series[ Simplify[q*T15b, q>0], {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jun 21 2018, fixed by Vaclav Kotesovec, Jul 03 2018 *)
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PROG
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(PARI) q='q+O('q^70); A=(eta(q)/eta(q^25))/q; B=eta(q^3)/(q^3*eta(q^75)); C = (eta(q^3)*eta(q^5)/(eta(q)*eta(q^15)))^3/q; D = (eta(q^3)/eta(q^15) )^2; T25A = A + 5/A; T15b = 2 + (-5 + T25A*(B + 5/B))*(-A + B)*(1/( B*A))^2*(D^3/C)/q^3; Vec(T15b) \\ G. C. Greubel, Jun 21 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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