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Search: id:A134178
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| A134178 |
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Expansion of chi(q) * chi(-q^2)^2 * chi(-q^4) * chi(q^6) * chi(-q^12)^2 / chi(-q^3) in powers of q where chi() is a Ramanujan theta function. |
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+0
1
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| 1, 1, -2, -2, 0, 1, 2, 0, 0, -1, -4, 0, 1, 0, 6, 2, 0, 1, -8, 0, 0, 0, 12, 0, -1, -1, -18, -4, 0, -1, 24, 0, 0, 2, -32, 0, 0, 1, 44, 6, 0, -2, -58, 0, 0, -1, 76, 0, 1, 2, -100, -8, 0, 1, 128, 0, 0, -3, -164, 0, 0, -1, 210, 12, 0, 4, -264, 0, 0, 2, 332, 0, -1, -5, -416, -18, 0, -2, 516, 0, 0, 5, -640, 0, -1, 2, 790, 24
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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Euler transform of period 24 sequence [ 1, -3, 0, -1, 1, -1, 1, 0, 0, -3, 1, -4, 1, -3, 0, 0, 1, -1, 1, -1, 0, -3, 1, 0, ...].
a(12*n+4) = a(12*n+7) = a(12*n+8) = a(12*n+11) = 0.
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EXAMPLE
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q^-3 + q^-1 - 2*q - 2*q^3 + q^7 + 2*q^9 - q^15 - 4*q^17 + q^21 + 6*q^25 + ...
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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)^4 * eta(x^3 + A) * eta(x^12 + A)^5/ (eta(x + A) * eta(x^4 + A)^2 * eta(x^6 + A)^3 * eta(x^8 + A) * eta(x^24 + A)^3), n))}
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CROSSREFS
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A029838(n) = a(4*n+1) = a(12*n). -2 * A083365(n) = a(4*n+2) = a(12*n+3).
Sequence in context: A108561 A104579 A079531 this_sequence A059018 A122190 A146093
Adjacent sequences: A134175 A134176 A134177 this_sequence A134179 A134180 A134181
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 11 2007
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