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A255320
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Expansion of chi(-x) * psi(x^3) * psi(x^48) in powers of x where chi(), psi() are Ramanujan theta functions.
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2
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1, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0
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OFFSET
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0,57
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(-19/3) * eta(q) * eta(q^6)^2 * eta(q^96)^2 / (eta(q^2) * eta(q^3) * eta(q^48)) in powers of q.
Euler transform of a period 96 sequence.
a(4*n + 2) = a(4*n + 3) = a(8*n + 4) = a(16*n + 9) = a(16*n + 13) = 0.
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EXAMPLE
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G.f. = 1 - x - x^5 + x^8 + x^16 - x^21 - x^33 + x^40 + x^48 - x^49 + ...
G.f. = q^19 - q^22 - q^34 + q^43 + q^67 - q^82 - q^118 + q^139 + q^163 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x, x^2] EllipticTheta[ 2, 0, x^(3/2)] EllipticTheta[2, 0, x^(24)] / (4 x^(51/8)), {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) * eta(x^6 + A)^2 * eta(x^96 + A)^2 / (eta(x^2 + A) * eta(x^3 + A) * eta(x^48 + A)), n))};
(PARI) {a(n) = my(A, p, e); if( n<0 || n%8 == 2, 0, A = factor(3*n + 19); 1/2 * prod( k=1, matsize(A)[1], [p, e] = A[k, ]; if( p<5, -(p+e==3), p%8 > 4, 1-e%2, e+1)))}; /* Michael Somos, Apr 24 2015 */
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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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