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A124242
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Expansion of parametrization of Ramanujan's continued fraction.
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0
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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; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 53
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FORMULA
| Euler transform of period 10 sequence [ -1, 1, 2, -1, -2, -1, 2, 1, -1, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= v^2 -(2-u)*(2-(2-u)*(2-v)).
Given g.f. A(x)=k, then (1-k)(k/(2-k))^2 = B(x), (1-k)^2((2-k)/k) = B(x^2) where B(x) = g.f. A078905.
G.f.: (f(-x, -x^9)f(-x^4, -x^6)f(-x^5, -x^5))/(f(-x^2, -x^8)f(-x^3, -x^7)^2) where f(a, b) is Ramanujan's two variable theta function.
G.f.: Product_{k>0} ((1-x^(10k-5))/((1-x^(10k-3))(1-x^(10k-7))))^2(1-x^(10k-1))(1-x^(10k-4))(1-x^(10k-6))(1-x^(10k-9))/((1-x^(10k-2))(1-x^(10k-8))).
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PROG
| (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, -1, -2, 1, 2, 1, -2, -1, 1][k%10+1]), n))}
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CROSSREFS
| A112274(n)=-a(n) if n>0.
Sequence in context: A029273 A117963 A112803 * A112274 A181391 A082054
Adjacent sequences: A124239 A124240 A124241 * A124243 A124244 A124245
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Oct 27 2006
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