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A132041
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Expansion of (eta(q) * eta(q^2) / (eta(q^5) * eta(q^10)))^2 in powers of q.
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4
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1, -2, -3, 6, 2, 2, -5, -16, 12, 2, 17, -10, -48, 56, 10, 24, -35, -126, 106, 14, 94, -70, -284, 296, 60, 152, -175, -620, 536, 80, 398, -320, -1243, 1218, 216, 652, -680, -2422, 2122, 328, 1435, -1190, -4470, 4240, 734, 2312, -2285, -8120, 7130, 1112, 4549, -3850, -14178, 13132, 2210
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OFFSET
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-1,2
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COMMENTS
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McKay-Thompson series of class 10C for Monster with a(0)=-2.
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LINKS
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FORMULA
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Euler transform of period 10 sequence [ -2, -4, -2, -4, 0, -4, -2, -4, -2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = 25 / f(t) where q = exp(2 Pi i t).
G.f.: (Product_{k>0} (1-x^k)* (1-x^(2k))/( (1-x^(5k))* (1-x^(10k))))^2.
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EXAMPLE
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G.f. = 1/q - 2 - 3*q + 6*q^2 + 2*q^3 + 2*q^4 - 5*q^5 - 16*q^6 + 12*q^7 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ 1/q (QPochhammer[ q] QPochhammer[ q^2] / (QPochhammer[ q^5] QPochhammer[ q^10]))^2, {q, 0, n}]; (* Michael Somos, Aug 26 2015 *)
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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( (eta(x + A) * eta(x^2 + A) / (eta(x^5 + A) * eta(x^10 + A)))^2, n))};
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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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