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A116915
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Expansion of f(-x,-x^4)^2/f(-x,-x^2) in powers of x.
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1
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1, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 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, 0, 0, 0, -1, 0, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
| Euler transform of period 5 sequence [ -1, 1, 1, -1, -1,...].
G.f.: Sum_{k} (-1)^k(x^((15k^2-7k)/2) -x^((15k^2+13k)/2+1)).
G.f.: Product_{k>0} (1-x^(5k))(1-x^(5k-1))(1-x^(5k-4))/((1-x^(5k-2))(1-x^(5k-3))).
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PROG
| (PARI) {a(n)=n=5*n+2; if(issquare(24*n+1, &n), -kronecker(12, n))}
(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))}
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CROSSREFS
| Cf. A010815(5n+2)=-a(n).
Sequence in context: A071003 A071002 A113431 * A076141 A011751 A093709
Adjacent sequences: A116912 A116913 A116914 * A116916 A116917 A116918
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Feb 26 2006
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