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Search: id:A113681
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| A113681 |
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Expansion of f(-x^2,-x^3)^2/f(-x,-x^2) 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.
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FORMULA
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Euler transform of period 5 sequence [1, -1, -1, 1, -1, ...].
G.f.: Sum_{k} (-1)^k(x^((15k^2-k)/2) +x^((15k^2-11k)/2+1)).
G.f.: Product_{k>0} (1-x^(5k))(1-x^(5k-2))(1-x^(5k-3))/((1-x^(5k-1))(1-x^(5k-4))).
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, n, (1-x^k)^((k%5==0)-kronecker(5, k)), 1+x*O(x^n)), n))}
(PARI) {a(n)=n*=5; if(issquare(24*n+1, &n), kronecker(12, n))}
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CROSSREFS
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Cf. A113430. A010815(5n)=a(n).
Adjacent sequences: A113678 A113679 A113680 this_sequence A113682 A113683 A113684
Sequence in context: A036987 A143259 A113430 this_sequence A155972 A010054 A106459
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Nov 04 2005
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