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A261202
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Expansion of phi(-x) * phi(-x^9) / f(-x^6)^2 in powers of x where phi(), f() are Ramanujan theta functions.
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2
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1, -2, 0, 0, 2, 0, 2, -4, 0, -4, 8, 0, 5, -14, 0, -8, 20, 0, 14, -28, 0, -20, 44, 0, 28, -66, 0, -40, 90, 0, 56, -124, 0, -80, 176, 0, 109, -244, 0, -144, 326, 0, 198, -432, 0, -268, 580, 0, 349, -772, 0, -456, 1004, 0, 600, -1300, 0, -780, 1692, 0, 1001
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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 q^(1/2) * eta(q)^2 * eta(q^9)^2 / (eta(q^2) * eta(q^6)^2 * eta(q^18)) in powers of q.
Euler transform of period 18 sequence [ -2, -1, -2, -1, -2, 1, -2, -1, -4, -1, -2, 1, -2, -1, -2, -1, -2, 0, ...].
a(3*n + 2) = 0.
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EXAMPLE
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G.f. = 1 - 2*x + 2*x^4 + 2*x^6 - 4*x^7 - 4*x^9 + 8*x^10 + 5*x^12 + ...
G.f. = 1/q - 2*q + 2*q^7 + 2*q^11 - 4*q^13 - 4*q^17 + 8*q^19 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x] EllipticTheta[ 4, 0, x^9] / QPochhammer[ x^6]^2, {x, 0, n}];
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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)^2 * eta(x^9 + A)^2 / (eta(x^2 + A) * eta(x^6 + A)^2 * eta(x^18 + A)), 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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