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A112165
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McKay-Thompson series of class 24h for the Monster group.
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5
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1, 1, -1, 1, 2, -1, -2, -1, 3, 0, -4, 1, 5, 1, -7, 0, 8, 0, -10, -1, 13, -2, -16, 0, 20, 3, -24, 2, 30, -2, -36, -4, 43, 0, -52, 3, 61, 2, -73, 1, 86, -1, -102, -3, 120, -4, -140, 1, 165, 8, -192, 5, 224, -6, -260, -10, 301, -2, -348, 7, 401, 7, -462, 2, 530, -2, -608, -8, 696, -10, -796, 3, 909, 18, -1035, 12
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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Expansion of chi(-x^4)^2 * chi(-x^12)^2 / (chi(-x^2) * chi(-x^6)) in powers of x where chi() is a Ramanujan theta function. - Michael Somos, Apr 22 2015
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EXAMPLE
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G.f. = 1 + x - x^2 + x^3 + 2*x^4 - x^5 - 2*x^6 - x^7 + 3*x^8 - 4*x^10 + ...
T24h = 1/q + q - q^3 + q^5 + 2*q^7 - q^9 - 2*q^11 - q^13 + 3*q^15 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ (QPochhammer[ x^2] QPochhammer[ x^6])^3 / (QPochhammer[ x] QPochhammer[ x^3] QPochhammer[ x^4]^2 QPochhammer[ x^12]^2), {x, 0, n}]; (* Michael Somos, Aug 31 2014 *)
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^6 + A)^3 / (eta(x + A) * eta(x^3 + A) * eta(x^4 + A)^2 * eta(x^12 + A)^2), n))}; /* Michael Somos, Aug 31 2014 */
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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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