Sequences containing all finite sequences

[hv at crypt.org]

"Robert G. Wilson v" <rgwv at rgwv.com> wrote:
:
:%I A000001
:%S A000001 1,1,1,2,1,1,1,1,2,2,1,3,1,1,1,1,1,1,2,1,2,1,2,1,1,1,3,2,2,3,1,4,1,1,1,
:%T A000001 1,1,1,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,3,1,2,2,2,1,2,1,3,1,2,2,1,3,1,
:%T A000001 1,1,4,2,3,3,2,4,1,5,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,2,1,1
:%N A000001 The permutations of all partitions of n in lexicographical order.
:%t A000001 Flatten[ Table[ Reverse[ # ] & /@ Reverse[ Sort[ Flatten[ Permutations[ 
:# ] & /@ Partitions[ n], 1]]], {n, 6}]] (from RGWv (rgwv at rgwv.com), Jun 22 2005)
:%Y A000001 Cf. .
:%O A000001 1,4
:%K A000001 nonn,tabl
:%A A000001

I think "combinatorial composition" is the correct term, at least
judging by http://mathworld.wolfram.com/Composition.html.
 
Hugo