A120031 Numerators of reduced forms of fractions obtained by performing the first n divisions shown below.

1, 1, 2, 5, 40, 4, 48, 312, 1664, 14144, 56576, 28288, 226304, 217600, 870400, 2524160, 80773120, 2375680, 1900544, 35160064, 1406402560, 28831252480, 115325009920, 288312524800, 4613000396800, 92260007936, 369040031744

Offset

0,3

Comments

1

-------

2*3

..-----

..4*5

....---

....6*.....

In other words, the successive fractions are

1,

1

-,

2

1..4

----,

.23.

1..45.

------,

.23..6

1..45..8

--------,

.23..67.

and so on

Suggested by a question from Ciprian Bonciocat (6 years old).

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = numerator of x(n) where x(0)=1, x(2n+1) = x(2n) (4n+1)/(4n+2), x(2n+2) = x(2n+1)(4n+4)/(4n+3). - Matthew Conroy Jun 26 2006

Example

1, 1/2, 2/3, 5/9, 40/63, 4/7, ...

Mathematica

a[0] = 1; a[n_] := a[n] = a[n - 1] If[OddQ[n], (2 n - 1)/(2 n), (2 n)/(2 n - 1)]; A120031[n_] := Numerator[a[n]]; Array[A120031, 26] (* JungHwan Min, Nov 08 2016 *)

Crossrefs

Cf. A120032.

Sequence in context: A183255 A307141 A109003 * A110066 A155176 A127974

Adjacent sequences: A120028 A120029 A120030 * A120032 A120033 A120034

Keyword

nonn,frac

Author

Mihai Cipu (mihai.cipu(AT)imar.ro), Jun 05 2006

Extensions

More terms from Matthew Conroy, Jun 26 2006

Status

approved