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A232166
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Expansion of phi(x) / psi(x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.
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1
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1, 2, -2, -4, 5, 6, -10, -12, 17, 24, -30, -40, 50, 62, -80, -100, 127, 160, -196, -244, 296, 360, -442, -532, 649, 786, -940, -1132, 1347, 1600, -1910, -2260, 2682, 3176, -3734, -4400, 5157, 6032, -7066, -8240, 9616, 11202, -13002, -15096, 17469, 20192
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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 4 sequence [ 2, -5, 2, 1, ...].
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EXAMPLE
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G.f. = 1 + 2*x - 2*x^2 - 4*x^3 + 5*x^4 + 6*x^5 - 10*x^6 - 12*x^7 + ...
G.f. = 1/q + 2*q - 2*q^3 - 4*q^5 + 5*q^7 + 6*q^9 - 10*q^11 -12*q^13 + ...
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MATHEMATICA
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a[ n_]:= SeriesCoefficient[4*x^(1/2)*EllipticTheta[3, 0, x]/EllipticTheta[ 2, 0, x]^2, {x, 0, n}];
a[ n_]:= SeriesCoefficient[QPochhammer[x^2]^7/(QPochhammer[x]^2* QPochhammer[x^4]^6), {x, 0, n}];
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^7 / (eta(x + A)^2 * eta(x^4 + A)^6), 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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