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Search: id:A113429
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| A113429 |
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Expansion of f(-x,-x^4) in powers of x. |
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+0
2
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| 1, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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FORMULA
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Euler transform of period 5 sequence [ -1, 0, 0, -1, -1, ...].
|a(n)| is the characteristic function of A085787.
G.f.: Prod_{k>0} (1-x^(5k))(1-x^(5k-1))(1-x^(5k-4)) = Sum_{k} (-1)^k x^((5k^2+3k)/2).
f(a,b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable theta function.
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, n, 1-x^k*[1, 1, 0, 0, 1][k%5+1], 1+x*O(x^n)), n))}
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CROSSREFS
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Sequence in context: A095901 A087049 A118009 this_sequence A133100 A077606 A004601
Adjacent sequences: A113426 A113427 A113428 this_sequence A113430 A113431 A113432
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 31 2005
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