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A281722
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Expansion of r(q) * s(q) in powers of q where r(), s() are cubic AGM functions.
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5
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1, 3, -18, 12, 21, -36, 36, 24, -90, 12, 54, -72, 84, 42, -144, 72, 93, -108, 36, 60, -252, 96, 108, -144, 180, 93, -252, 12, 168, -180, 216, 96, -378, 144, 162, -288, 84, 114, -360, 168, 270, -252, 288, 132, -504, 72, 216, -288, 372, 171, -558, 216, 294, -324
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Expansion of eta(q)^3 * (eta(q)^3 + 9 * eta(q^9)^3) / eta(q^3)^2 in powers of q.
G.f. is a period 1 Fourier series which satisfies f(-1 / (9 t)) = 81 (t/i)^2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A144614.
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EXAMPLE
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G.f. = 1 + 3*q - 18*q^2 + 12*q^3 + 21*q^4 - 36*q^5 + 36*q^6 + 24*q^7 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ q]^3 (QPochhammer[ q]^3 + 9 q QPochhammer[ q^9]^3) / QPochhammer[ q^3]^2, {q, 0, n}];
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PROG
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(PARI) {a(n) = if( n<0, 0, my(A = x * O(x^n)); polcoeff( eta(x + A)^3 * (eta(x + A)^3 + 9 * x * eta(x^9 + A)^3) / eta(x^3 + 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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