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Search: id:A112803
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| A112803 |
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Expansion of parametrization of Ramanujan's continued fraction. |
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1
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| 1, 1, -1, -1, 2, 0, -2, 2, 1, -4, 1, 4, -4, -1, 6, -3, -6, 7, 3, -10, 4, 10, -12, -6, 18, -5, -18, 20, 8, -30, 10, 29, -31, -12, 46, -17, -44, 47, 20, -68, 23, 66, -72, -31, 104, -33, -98, 107, 44, -156, 51, 144, -154, -61, 220, -75, -206, 220, 90, -310, 104, 290, -312, -131, 442, -143, -408, 437, 178, -618, 202
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 53
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FORMULA
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Euler transform of period 10 sequence [1, -2, 0, 2, -2, 2, 0, -2, 1, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)=(2-v)^2-u*(2-u*v).
Given g.f. k=A(x) then (k-1)((2-k)/k)^2 = B(x), (k-1)^2(k/(2-k)) = B(x^2) where B(x) = g.f. A078905.
G.f.: Product_{k>0} ((1-x^(10k-2))(1-x^(10k-5))(1-x^(10k-8))^2)/((1-x^(10k-1))(1-x^(10k-4))^2(1-x^(10k-6))^2(1-x^(10k-9))).
G.f.: (f(-x^5, -x^5)f(-x^2, -x^8)^2)/(f(-x, -x^9)f(-x^4, -x^6)^2) whe re f(a, b) is Ramanujan's two variable theta function.
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( prod(k=1, n, (1-x^k+A)^[0, -1, 2, 0, -2, 2, -2, 0, 2, -1][k%10+1]), n))}
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CROSSREFS
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A112274(n)=a(n) if n>0.
Sequence in context: A083817 A029273 A117963 this_sequence A124242 A112274 A082054
Adjacent sequences: A112800 A112801 A112802 this_sequence A112804 A112805 A112806
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Sep 19 2005
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