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Search: id:A113430
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| A113430 |
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Expansion of f(-x)f(-x^10)/f(-x^2,-x^8) in powers of x. |
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+0
2
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| 1, -1, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 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, 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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COMMENT
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f(a,b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable theta function and f(-x):=f(-x,-x^2).
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FORMULA
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Euler transform of period 10 sequence [ -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, ...].
|a(n)| is the characteristic function of A093722.
G.f.: Prod_{k>0} (1-x^k)/((1-x^(10k-2))(1-x^(10k-8))) = Sum_{k} x^((15k^2+k)/2) -x^((15k^2-11k+2)/2).
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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, 1, 1, 1, 1, 1, 0, 1][k%10+1], 1+x*O(x^n)), n))}
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CROSSREFS
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Sequence in context: A154269 A036987 A143259 this_sequence A113681 A155972 A010054
Adjacent sequences: A113427 A113428 A113429 this_sequence A113431 A113432 A113433
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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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