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A182034
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Expansion of c(q^2)^2 / (c(q) * c(q^3)) in powers of q where c() is a cubic AGM theta function.
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4
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1, -1, 1, 0, 1, -2, 0, 0, 1, 0, -2, 4, 0, 2, -8, 0, 1, 2, 0, -4, 14, 0, 4, -24, 0, 1, 6, 0, -8, 38, 0, 8, -63, 0, 2, 16, 0, -14, 92, 0, 14, -150, 0, 4, 36, 0, -24, 208, 0, 23, -329, 0, 6, 78, 0, -40, 440, 0, 38, -684, 0, 10, 160, 0, -63, 884, 0, 60, -1358, 0
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OFFSET
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0,6
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COMMENTS
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LINKS
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FORMULA
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Expansion of (chi(-q^3)^2 * psi(q^3)^4) / (psi(q) * f(-q^9)^3) in powers of q where psi(), chi(), f() are Ramanujan theta functions. - Michael Somos, May 20 2015
Expansion of eta(q) * eta(q^6)^6 / (eta(q^2)^2 * eta(q^3)^2 * eta(q^9)^3) in powers of q.
Euler transform of period 18 sequence [ -1, 1, 1, 1, -1, -3, -1, 1, 4, 1, -1, -3, -1, 1, 1, 1, -1, 0, ...].
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EXAMPLE
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G.f. = 1 - q + q^2 + q^4 - 2*q^5 + q^8 - 2*q^10 + 4*q^11 + 2*q^13 - 8*q^14 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ (2 q^(1/8) QPochhammer[ q^6]^6) / (QPochhammer[ q^9]^3 EllipticTheta[ 2, 0, q^(1/2)] QPochhammer[ q^3]^2), {q, 0, n}]; (* Michael Somos, May 20 2015 *)
a[ n_] := SeriesCoefficient[ (QPochhammer[ q^3] EllipticTheta[ 2, 0, q^(3/2)]^3) / (4 q QPochhammer[ q^9]^3 EllipticTheta[ 2, 0, q^(1/2)]), {q, 0, n}]; (* Michael Somos, May 20 2015 *)
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PROG
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(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^6 + A)^6 / (eta(x^2 + A)^2 * eta(x^3 + A)^2 * eta(x^9 + A)^3), 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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