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Search: id:A143251
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| A143251 |
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Expansion of f(-x, -x^7) * f(-x^2, -x^6) in powers of x where f(,) is Ramanujan's two variable theta function. |
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+0
1
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| 1, -1, -1, 1, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, -1, 2, 0, -1, 0, 0, -2, -1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, -1, -1, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, -1, 0, -1, 0, 1, -1, -1, 0, 0, 0, 0, -1, 0, -1, 1, 0, 0, 1, 0, 0, 2, -1, 0, 1, 1, 0, 0, -1, 0, 0, -1, -1, 0, -1, 0, 2, 1, 0, -1, 2, 0, 0, 0, 0, 1, 0, 0, -1, -1, -1, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,23
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FORMULA
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Euler transform of period 8 sequence [ -1, -1, 0, 0, 0, -1, -1, -2, ...].
G.f.: Product_{k>0} (1 - x^(8*k))^2 * (1 - x^(8*k - 1)) * (1 - x^(8*k - 2)) * (1 - x^(8*k - 6)) * (1 - x^(8*k - 7)).
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EXAMPLE
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q^13 - q^29 - q^45 + q^61 - q^109 + q^157 + q^173 - q^269 - q^317 + ...
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PROGRAM
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(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k)^([2, 1, 1, 0, 0, 0, 1, 1][k%8 + 1]), 1 + x * O(x^n)), n))}
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CROSSREFS
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Sequence in context: A104451 A106602 A106594 this_sequence A115235 A160973 A036853
Adjacent sequences: A143248 A143249 A143250 this_sequence A143252 A143253 A143254
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 01 2008
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