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Search: id:A134079
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| A134079 |
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Expansion of q^(-2/3)*c(-q)^2/9 in powers of q where c(q) is a cubic AGM analog function. |
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2
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| 1, -2, 5, -4, 8, -6, 14, -8, 14, -10, 21, -16, 20, -14, 28, -16, 31, -18, 40, -20, 32, -28, 42, -24, 38, -32, 62, -28, 44, -30, 56, -40, 57, -34, 70, -36, 72, -38, 70, -48, 62, -52, 85, -44, 68, -46, 112, -56, 74, -50, 100, -64, 80, -64, 98, -56, 108, -58, 124, -60, 112, -76, 112, -64, 98, -66, 155, -80, 104
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of ( f(q^3)^3 / f(q) )^2 in powers of q where f() is a Ramanujan theta function.
Expansion of (-q)^(-2/3) * ( eta(3 * (t + 1/2) )^3 / eta(t + 1/2) )^2 in powers of q = exp(2 pi i t).
Euler transform of period 12 sequence [ -2, 4, 4, 2, -2, -8, -2, 2, 4, 4, -2, -4, ...].
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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 + A) * eta(x^4 + A) * eta(x^6 + A)^9 / ( eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A) )^3 )^2, n))}
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CROSSREFS
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(-1)^n * A033686(n) = a(n). A134078(3*n+2) = 18 * a(n).
Adjacent sequences: A134076 A134077 A134078 this_sequence A134080 A134081 A134082
Sequence in context: A093052 A081556 A033686 this_sequence A080031 A065221 A114752
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 06 2007
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