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A058096
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McKay-Thompson series of class 9d for Monster.
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3
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1, 0, -3, 2, 0, 6, 5, 0, 3, 6, 0, -18, 12, 0, 21, 16, 0, 6, 27, 0, -60, 34, 0, 72, 51, 0, 24, 70, 0, -168, 101, 0, 183, 134, 0, 54, 182, 0, -411, 240, 0, 450, 322, 0, 138, 416, 0, -936, 544, 0, 981, 696, 0, 282, 902, 0, -1989, 1144, 0, 2070, 1462, 0, 597, 1832
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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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G.f. is a period 1 Fourier series which satisfies f(-1 / (81 t)) = f(t) where q = exp(2 Pi i t). - Michael Somos, Aug 28 2015
Expansion of A - 3/A, where A = (eta(q^9)^2/(eta(q^3)*eta(q^27)))^2, in powers of q. - G. C. Greubel, Jun 03 2018
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EXAMPLE
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T9d = 1/q - 3*q + 2*q^2 + 6*q^4 + 5*q^5 + 3*q^7 + 6*q^8 - 18*q^10 + 12*q^11 + ...
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MATHEMATICA
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a[ n_] := With[ {A = 1/q (QPochhammer[ q^9]^2 / (QPochhammer[ q^3] QPochhammer[ q^27]))^2}, seriesCoefficient[ A - 3 / A, {q, 0, n}]]; (* Michael Somos, Aug 28 2015 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A := (eta[q^9]^2/(eta[q^3]*eta[q^27]) )^2; a := CoefficientList[Series[q*(A - 3/A), {q, 0, 60}], q];
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PROG
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(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = eta(x^9 + A)^4 / (eta(x^3 + A) * eta(x^27 + A))^2; polcoeff( A - 3 * x^2 / A, n))}; /* Michael Somos, Aug 28 2015 */
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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