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A258092
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Expansion of f(x, x^2) / psi(x)^3 in powers of x where psi(), f(, ) are Ramanujan theta functions.
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2
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1, -2, 4, -10, 20, -36, 64, -112, 189, -308, 492, -778, 1210, -1844, 2776, -4144, 6114, -8914, 12884, -18484, 26302, -37124, 52040, -72512, 100415, -138196, 189160, -257648, 349184, -470932, 632312, -845472, 1125853, -1493222, 1973060, -2597892, 3408754
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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^3)^2 / (eta(q^2)^5 * eta(q^6)) in powers of q.
Euler transform of period 6 sequence [-2, 3, -4, 3, -2, 2, ...].
G.f.: Product_{k>0} (1 - x^(3*k)) / ((1 + x^(3*k)) * (1 + x^k)^2 * (1 - x^(2*k))^3).
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EXAMPLE
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G.f. = 1 - 2*x + 4*x^2 - 10*x^3 + 20*x^4 - 36*x^5 + 64*x^6 - 112*x^7 + ...
G.f. = 1/q - 2*q^2 + 4*q^5 - 10*q^8 + 20*q^11 - 36*q^14 + 64*q^17 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x]^2 QPochhammer[ x^3]^2 / ( QPochhammer[ x^2]^5 QPochhammer[ x^6]), {x, 0, n}]; (* Michael Somos, May 25 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 + A)^2 * eta(x^3 + A)^2 / (eta(x^2 + A)^5 * eta(x^6 + 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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