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A262614
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Expansion of phi(-x^3) * f(-x, -x^5) / psi(x) in powers of x where phi(), psi(), f(, ) are Ramanujan theta functions.
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3
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1, -2, 2, -5, 9, -12, 16, -23, 36, -47, 60, -84, 115, -149, 188, -245, 321, -406, 505, -641, 813, -1007, 1237, -1533, 1901, -2321, 2816, -3437, 4191, -5055, 6068, -7307, 8792, -10501, 12490, -14886, 17720, -20975, 24755, -29236, 34492, -40522, 47486, -55666
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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 f(-x^3)^3 / (f(x, x^2) * psi(x)) in powers of x where psi(), f(, ) are Ramanujan theta functions.
Expansion of q^(-5/24) * eta(q)^2 * eta(q^3) * eta(q^6) / eta(q^2)^3 in powers of q.
Euler transform of period 6 sequence [ -2, 1, -3, 1, -2, -1, ...].
a(n) ~ (-1)^n * exp(sqrt(n/2)*Pi) / (6*sqrt(n)). - Vaclav Kotesovec, Apr 17 2016
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EXAMPLE
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G.f. = 1 - 2*x + 2*x^2 - 5*x^3 + 9*x^4 - 12*x^5 + 16*x^6 - 23*x^7 +
G.f. = q^5 - 2*q^29 + 2*q^53 - 5*q^77 + 9*q^101 - 12*q^125 + 16*q^149 - 23*q^173 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ 2 x^(1/8) QPochhammer[ x^3]^3 QPochhammer[ x, x^2] / (EllipticTheta[ 4, 0, x^3] EllipticTheta[ 2, 0, x^(1/2)]), {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 + A)^2 * eta(x^3 + A) * eta(x^6 + A) / eta(x^2 + A)^3, 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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