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A260514
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Expansion of phi(x) * chi(x^2)^4 in powers of x where phi(), chi() are Ramanujan theta functions.
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2
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1, 2, 4, 8, 8, 12, 16, 16, 29, 36, 44, 64, 72, 88, 112, 128, 162, 202, 244, 304, 352, 420, 496, 576, 703, 820, 968, 1152, 1320, 1544, 1792, 2048, 2405, 2782, 3204, 3728, 4240, 4856, 5568, 6320, 7259, 8276, 9416, 10752, 12144, 13760, 15568, 17536, 19875, 22416
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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^(1/3) * eta(q^2) * eta(q^4)^6 / (eta(q)^2 * eta(q^8)^4) in powers of q.
Euler transform of period 8 sequence [ 2, 1, 2, -5, 2, 1, 2, -1,...].
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EXAMPLE
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G.f. = 1 + 2*x + 4*x^2 + 8*x^3 + 8*x^4 + 12*x^5 + 16*x^6 + 16*x^7 +...
G.f. = 1/q + 2*q^2 + 4*q^5 + 8*q^8 + 8*q^11 + 12*q^14 + 16*q^17 +...
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MATHEMATICA
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a[ n_]:= SeriesCoefficient[ EllipticTheta[ 3, 0, x] QPochhammer[ -x^2, x^4]^4, {x, 0, n}];
nmax=60; CoefficientList[Series[Product[(1+x^k) * (1-x^(4*k))^6 / ((1-x^k) * (1-x^(8*k))^4), {k, 1, nmax}], {x, 0, nmax}], x] (*Vaclav Kotesovec,Oct 14 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^2 + A) * eta(x^4 + A)^6 / (eta(x + A)^2 * eta(x^8 + A)^4), n))};
(PARI) q='q+O('q^99); Vec(eta(q^2)*eta(q^4)^6/(eta(q)^2*eta(q^8)^4)) \\Altug Alkan,Aug 01 2018
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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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