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A263021
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Expansion of f(-x^3)^6 / (phi(-x) * phi(-x^3)) in powers of x where phi(), f() are Ramanujan theta functions.
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3
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1, 2, 4, 4, 6, 8, 9, 10, 8, 14, 14, 16, 16, 16, 20, 18, 22, 24, 21, 26, 28, 28, 28, 24, 36, 34, 36, 38, 32, 32, 40, 42, 44, 36, 46, 56, 43, 50, 40, 52, 54, 56, 54, 42, 60, 62, 64, 64, 56, 66, 56, 72, 70, 56, 74, 74, 76, 72, 64, 80, 81, 84, 84, 64, 76, 88, 88
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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^(-3/4) * eta(q^2) * eta(q^3)^4 * eta(q^6) / eta(q)^2 in powers of q.
Euler transform of period 6 sequence [ 2, 1, -2, 1, 2, -4, ...].
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EXAMPLE
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G.f. = 1 + 2*x + 4*x^2 + 4*x^3 + 6*x^4 + 8*x^5 + 9*x^6 + 10*x^7 + 8*x^8 + ...
G.f. = q^3 + 2*q^7 + 4*q^11 + 4*q^15 + 6*q^19 + 8*q^23 + 9*q^27 + 10*q^31 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x^3]^6 / (EllipticTheta[ 4, 0, x] EllipticTheta[ 4, 0, x^3]), {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^2 + A) * eta(x^3 + A)^4 * eta(x^6 + A) / eta(x + A)^2, n))};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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