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A261394
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Expansion of phi(q)^4 / phi(q^3) in powers of q where phi() is a Ramanujan theta function.
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2
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1, 8, 24, 30, 8, 0, 36, 48, 24, 32, 48, 48, 30, 0, 48, 72, 8, 48, 96, 48, 0, 0, 96, 96, 36, 56, 48, 102, 48, 0, 120, 48, 24, 72, 48, 96, 32, 0, 96, 120, 48, 48, 144, 144, 48, 0, 96, 96, 30, 56, 120, 144, 0, 0, 108, 96, 48, 120, 144, 48, 72, 0, 144, 192, 8, 96
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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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Euler transform of period 12 sequence [ 8, -12, 6, -4, 8, -9, 8, -4, 6, -12, 8, -3, ...].
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EXAMPLE
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G.f. = 1 + 8*x + 24*x^2 + 30*x^3 + 8*x^4 + 36*x^6 + 48*x^7 + 24*x^8 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q]^4 / EllipticTheta[ 3, 0, q^3], {q, 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)^20 * eta(x^3 + A)^2 * eta(x^12 + A)^2 / (eta(x + A)^8 * eta(x^4 + A)^8 * eta(x^6 + A)^5), 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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