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Search: id:A139137
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| A139137 |
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Expansion of phi(q) / phi(q^3) in powers of q where phi() is a Ramanujan theta function. |
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3
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| 1, 2, 0, -2, -2, 0, 4, 4, 0, -6, -8, 0, 10, 12, 0, -16, -18, 0, 24, 28, 0, -36, -40, 0, 52, 58, 0, -74, -84, 0, 104, 116, 0, -144, -160, 0, 198, 220, 0, -268, -296, 0, 360, 396, 0, -480, -528, 0, 634, 694, 0, -832, -908, 0, 1084, 1184, 0, -1404, -1528, 0, 1808, 1964, 0, -2316, -2514, 0, 2952, 3196
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OFFSET
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0,2
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FORMULA
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Expansion of eta(q^2)^5 * eta(q^3)^2 * eta(q^12)^2 / (eta(q)^2 * eta(q^4)^2 * eta(q^6)^5) in powers of q.
Euler transform of period 12 sequence [ 2, -3, 0, -1, 2, 0, 2, -1, 0, -3, 2, 0, ...].
a(3*n + 2) = 0.
G.f. is a period 1 Fourier series which satisfies f(-1/(12 t)) = 3^(1/2) / f(t) where q = exp(2 pi i t).
G.f.: (Sum_k x^k^2) / (Sum_k x^(3*k^2)).
G.f.: Product_{k>0} P(12, x^k)^2 / (P(3, x^k) * P(6, x^k)^3) where P(n, x) is nth cyclotomic polynomial.
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EXAMPLE
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1 + 2*q - 2*q^3 - 2*q^4 + 4*q^6 + 4*q^7 - 6*q^9 - 8*q^10 + 10*q^12 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^3 + A)^2 * eta(x^12 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^6 + A)^5), n))}
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CROSSREFS
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A132002(n) = a(3*n). 2 * A139135(n) = a(3*n + 1).
Sequence in context: A035692 A121363 A138021 this_sequence A138231 A076880 A082115
Adjacent sequences: A139134 A139135 A139136 this_sequence A139138 A139139 A139140
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 10 2008
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