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%I #9 Nov 08 2016 22:25:00
%S 1,1,2,5,40,4,48,312,1664,14144,56576,28288,226304,217600,870400,
%T 2524160,80773120,2375680,1900544,35160064,1406402560,28831252480,
%U 115325009920,288312524800,4613000396800,92260007936,369040031744
%N Numerators of reduced forms of fractions obtained by performing the first n divisions shown below.
%C 1
%C -------
%C 2*3
%C ..-----
%C ..4*5
%C ....---
%C ....6*.....
%C In other words, the successive fractions are
%C 1,
%C 1
%C -,
%C 2
%C 1..4
%C ----,
%C .23.
%C 1..45.
%C ------,
%C .23..6
%C 1..45..8
%C --------,
%C .23..67.
%C and so on
%C Suggested by a question from Ciprian Bonciocat (6 years old).
%F 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
%e 1, 1/2, 2/3, 5/9, 40/63, 4/7, ...
%t 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 *)
%Y Cf. A120032.
%K nonn,frac
%O 0,3
%A Mihai Cipu (mihai.cipu(AT)imar.ro), Jun 05 2006
%E More terms from _Matthew Conroy_, Jun 26 2006
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