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Search: id:A134078
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| A134078 |
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Expansion of (phi(-q) / phi(-q^2))^3 * phi(q^3)^5 / phi(-q^6) in powers of q where phi() is a Ramanujan theta function. |
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3
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| 1, -6, 18, -34, 42, -36, 30, -48, 90, -118, 108, -72, 54, -84, 144, -204, 186, -108, 66, -120, 252, -272, 216, -144, 102, -186, 252, -370, 336, -180, 180, -192, 378, -408, 324, -288, 90, -228, 360, -476, 540, -252, 240, -264, 504, -708, 432, -288, 198, -342, 558, -612, 588, -324, 174, -432, 720, -680, 540, -360
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Euler transform of period 12 sequence [ -6, 3, 4, 0, -6, -10, -6, 0, 4, 3, -6, -4, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (12 t)) = 8 (t/i)^2 g(t) where q = exp(2 pi i t) and g() is g.f. for A133739.
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EXAMPLE
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1 - 6*q + 18*q^2 - 34*q^3 + 42*q^4 - 36*q^5 + 30*q^6 - 48*q^7 + ...
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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)^6 * eta(x^4 + A)^3 * eta(x^6 + A)^23 / ( eta(x^2 + A)^9 * eta(x^3 + A)^10 * eta(x^12 + A)^9 ), n))}
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CROSSREFS
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-36 * A098098(n) = a(6*n+5). 18 * A134079(n) = a(3*n+2).
Adjacent sequences: A134075 A134076 A134077 this_sequence A134079 A134080 A134081
Sequence in context: A017593 A096286 A110671 this_sequence A038343 A110965 A111147
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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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