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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
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
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.)