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 A120031 Numerators of reduced forms of fractions obtained by performing the first n divisions shown below. 31
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)