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Search: id:A132225
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| A132225 |
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Expansion of (phi(q) - phi(q^5)) / (phi(q) + phi(q^5)) in powers of q where phi() is a Ramanujan theta function. |
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+0
1
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| 1, -1, 1, 0, -2, 2, -2, 1, 2, -3, 4, -4, 1, 2, -5, 8, -7, 3, 2, -10, 14, -12, 6, 6, -17, 22, -20, 8, 10, -26, 35, -31, 12, 14, -39, 54, -47, 20, 20, -61, 82, -72, 31, 32, -93, 122, -107, 44, 50, -133, 176, -154, 61, 68, -189, 254, -220, 90, 94, -272, 362, -312, 131, 136, -385, 504, -437, 178, 194, -530
(list; graph; listen)
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OFFSET
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1,5
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REFERENCES
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S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 26
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FORMULA
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Expansion of R(q)* R(q^4) in powers of q where R(q) is the Rogers-Ramanujan continued fraction, g.f. A007325
Euler transform of period 20 sequence [ -1, 1, 1, -2, 0, -1, 1, 2, -1, 0, -1, 2, 1, -1, 0, -2, 1, 1, -1, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (1 - u*v^3) * (u^3 -v) + 3 * u * v * (1 - u^2) * (1 - v^2) - 3 * u * v * (1 - u * v) * (u - v).
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v, w) = (1 + u * v^3) * (u^3 + v) - (1 + u^2 * v^2) * (u^2 + v^2) - 3 * u * v * (1 + u^2) * (1 + v^2) + 5 * u * v * (1 + u * v) * (u + v) - 10 * u^2 * v^2.
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EXAMPLE
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q - q^2 + q^3 - 2*q^5 + 2*q^6 - 2*q^7 + q^8 + 2*q^9 - 3*q^10 + ...
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PROGRAM
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(PARI) {a(n) = if(n<1, 0, n--; polcoeff( prod(k = 1, n, (1 -x^k +x*O(x^n))^ [0, 1, -1, -1, 2, 0, 1, -1, -2, 1, 0, 1, -2, -1, 1, 0, 2, -1, -1, 1][k%20+1]), n))}
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CROSSREFS
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Sequence in context: A056691 A130790 A029330 this_sequence A093116 A124369 A138258
Adjacent sequences: A132222 A132223 A132224 this_sequence A132226 A132227 A132228
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 14 2007
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