A270124 Ratios of successive terms of A270121.

2, 16, 3600, 4354563600, 30582275103386435842563600, 8210597206238423089030527211173884373017314096293353169731842563600

Offset: 0

Author

Andrew Hone, Mar 11 2016

Keywords

• nonn

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.

Programs

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 *)

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.