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A058533
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McKay-Thompson series of class 18C for the Monster group.
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5
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1, 0, 3, -2, 3, -6, 10, -12, 15, -22, 30, -36, 44, -60, 78, -96, 117, -150, 190, -228, 276, -340, 420, -504, 603, -732, 885, -1052, 1245, -1488, 1770, -2088, 2454, -2902, 3420, -3996, 4666, -5460, 6378, -7400, 8583, -9972, 11566, -13344, 15378, -17752, 20448
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OFFSET
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-1,3
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COMMENTS
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LINKS
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FORMULA
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Expansion of -1 + psi(q) / (q * psi(q^9)) + 3 * q * psi(q^9) / psi(q) in powers of q where psi() is a Ramanujan theta function. - Michael Somos, Aug 09 2012
a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017
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EXAMPLE
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T18C = 1/q + 3*q - 2*q^2 + 3*q^3 - 6*q^4 + 10*q^5 - 12*q^6 + 15*q^7 - ...
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MATHEMATICA
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QP = QPochhammer; s = -q + QP[q^3]^6 / (QP[q]*QP[q^2]*QP[q^6]^2*QP[q^9]* QP[q^18]) + O[q]^50; CoefficientList[s, q] (* Jean-François Alcover, Nov 12 2015, adapted from PARI *)
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PROG
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(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( -x + eta(x^3 + A)^6 / (eta(x + A) * eta(x^2 + A) * eta(x^6 + A)^2 * eta(x^9 + A) * eta(x^18 + A)), n))}; /* Michael Somos, Aug 09 2012 */
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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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