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Search: id:A134005
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| A134005 |
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Expansion of (chi(-q) * chi(-q^19))^2 in powers of q where chi() is a Ramanujan theta function. |
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+0
2
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| 1, -2, 1, -2, 4, -4, 5, -6, 9, -12, 13, -16, 21, -26, 29, -36, 46, -54, 62, -76, 94, -108, 126, -150, 179, -210, 239, -282, 335, -384, 440, -512, 597, -684, 781, -902, 1041, -1186, 1347, -1544, 1768, -2006, 2268, -2584, 2941, -3318, 3742, -4236, 4792, -5392, 6053, -6820, 7681, -8604, 9632
(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 q^(5/3) * ( eta(q) * eta(q^19) / (eta(q^2) * eta(q^38)))^2 in powers of q.
Euler transform of period 38 sequence [ -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -4, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (342 t)) = 4 / f(t) where q = exp(2 pi i t).
G.f.: (Product_{k>0} (1 + x^k) * (1 + x^(19*k)))^-2.
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EXAMPLE
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q^-5 - 2*q^-2 + q - 2*q^4 + 4*q^7 - 4*q^10 + 5*q^13 - 6*q^16 + 9*q^19 - ...
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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^19 + A) / eta(x^2 + A) / eta(x^38 + A) )^2, n))}
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CROSSREFS
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A112199(n) = - A134004(n-2) - a(2*n+1) / 2. Convolution inverse of A134004.
Sequence in context: A132965 A022597 A073252 this_sequence A132320 A076369 A072727
Adjacent sequences: A134002 A134003 A134004 this_sequence A134006 A134007 A134008
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 01 2007
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