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 A270124 Ratios of successive terms of A270121. 2
 2, 16, 3600, 4354563600, 30582275103386435842563600, 8210597206238423089030527211173884373017314096293353169731842563600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The ratios A270121(n+1)/A270121(n) generate the sequence for n>=1. LINKS Table of n, a(n) for n=0..5. A. N. W. Hone, Curious continued fractions, nonlinear recurrences and transcendental numbers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.8.4. A. N. W. Hone, Continued fractions for some transcendental numbers, arXiv:1509.05019 [math.NT], 2015-2016, Monatsh. Math. DOI: 10.1007/s00605-015-0844-2. FORMULA A270121 is generated by a recurrence of second order: if A270121(n)=x(n) then x(n+1)*x(n-1)=x(n)^2*(1+n*x(n)) for n>=1 with x(1)=7,x(2)=112. MATHEMATICA (* b = A270121 *) b[1] = 7; b[2] = 112; b[n_] := b[n] = (b[n - 1]^2 (1 + (n - 1) b[n - 1]))/b[n - 2]; a[0] = 2; a[n_] := b[n + 1]/b[n]; Table[a[n], {n, 0, 5}] (* Jean-François Alcover, Dec 16 2018 *) CROSSREFS Sequence in context: A203315 A158506 A167435 * A138834 A088321 A061301 Adjacent sequences: A270121 A270122 A270123 * A270125 A270126 A270127 KEYWORD nonn AUTHOR Andrew Hone, Mar 11 2016 STATUS approved

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Last modified July 15 22:54 EDT 2024. Contains 374334 sequences. (Running on oeis4.)