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Search: id:A113407
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| A113407 |
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Expansion of psi(x)phi(x^2) where psi(),phi() are Ramanujan theta functions. |
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+0
5
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| 1, 1, 2, 3, 0, 2, 1, 0, 4, 2, 1, 2, 2, 0, 2, 1, 0, 2, 4, 2, 0, 3, 0, 4, 2, 0, 0, 0, 3, 2, 2, 0, 2, 4, 0, 2, 3, 0, 4, 2, 0, 0, 2, 0, 2, 1, 2, 4, 0, 0, 2, 2, 0, 6, 2, 1, 2, 2, 0, 0, 4, 0, 0, 4, 0, 2, 1, 0, 4, 0, 0, 2, 2, 4, 2, 2, 0, 2, 5, 0, 2, 0, 2, 0, 2, 0, 4, 4, 0, 0, 0, 1, 0, 4, 0, 2, 2, 0, 4, 4, 2, 2, 0, 0, 2
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 114 Entry 8(vi).
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FORMULA
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Euler transform of period 8 sequence [1, 1, 1, -4, 1, 1, 1, -2, ...].
Expansion of q^(-1/8) eta(q^4)^5/(eta(q)eta(q^8)^2) in powers of q.
a(9n+4)=a(9n+7)=0. a(9n+1)=a(n).
G.f.: (Sum_{k} x^(2k^2))(Sum_{k>=0} x^((k^2+k)/2)) = Sum_{k>=0} (-1)^k (x^(2k+1)+1)/(x^(2k+1)-1) x^((k^2+k)/2).
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^4+A)^5/eta(x+A)/eta(x^8+A)^2, n))}
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CROSSREFS
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Sequence in context: A065861 A126832 A068908 this_sequence A039703 A103180 A126045
Adjacent sequences: A113404 A113405 A113406 this_sequence A113408 A113409 A113410
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Oct 28 2005
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