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 A124242 Expansion of a parametrization of Ramanujan's continued fraction. 3
 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; text; internal format)
 OFFSET 0,5 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). REFERENCES Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 53 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions 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 B(x) = (1-k) * (k / (2-k))^2, B(x^2) = (1-k)^2 * ((2-k) / k) where B(x) is the g.f. for A078905. Expansion of f(-x^5, -x^10)^3 / (f(x, x^4) * f(-x^3, -x^7)^2) in powers of x where f(, ) is Ramanujan's general theta function. - Michael Somos, Jan 06 2016 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))). -a(n) = A112274(n) unless n = 0. G.f.: 1 - r(q) * r(q^2)^2 where r() is the Rogers-Ramanujan continued fraction. - Seiichi Manyama, Apr 18 2017 EXAMPLE G.f. = 1 - x + x^2 + x^3 - 2*x^4 + 2*x^6 - 2*x^7  - x^8 + 4*x^9 - x^10 - 4*x^11 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ Product[ (1 - x^k)^{ 1, -1, -2, 1, 2, 1, -2, -1, 1, 0}[[Mod[k, 10, 1]]], {k, n}], {x, 0, n}]; (* Michael Somos, Jan 06 2016 *) PROG (PARI) {a(n) = my(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))}; CROSSREFS Cf. A078905, A112274, A112803, A285348. Sequence in context: A117963 A321594 A112803 * A112274 A336891 A181391 Adjacent sequences:  A124239 A124240 A124241 * A124243 A124244 A124245 KEYWORD sign AUTHOR Michael Somos, Oct 27 2006 STATUS approved

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Last modified June 16 14:05 EDT 2021. Contains 345057 sequences. (Running on oeis4.)