This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A124773 #3 Mar 30 2012 17:35:17
%S A124773 1,1,1,1,2,2,1,1,6,6,3,3,2,2,1,1,24,24,12,12,8,8,4,4,6,6,3,3,2,2,1,1,
%T A124773 120,120,60,60,40,40,20,20,30,30,15,15,10,10,5,5,24,24,12,12,8,8,4,4,
%U A124773 6,6,3,3,2,2,1,1,720,720,360,360,240,240,120,120,180,180,90,90,60,60,30
%N A124773 Number of permutations associated with compositions in standard order.
%C A124773 The standard order of compositions is given by A066099.
%C A124773 Arrange the cycles of the permutation by the smallest member of each cycle and read off the cycle sizes. E.g., for (1)(24)(3), the associated composition is 1,2,1.
%F A124773 For composition b(1),...,b(k), a(n) = Product_{i=1}^n C((Sum_{j=i}^n b(j)) - 1, b(i)-1) * (b(i)-1)!.
%e A124773 Composition number 11 is 2,1,1; the associated permutations are (12)(3)(4), (13)(2)(4) and (14)(2)(3), so a(11) = 3.
%e A124773 The table starts:
%e A124773 1
%e A124773 1
%e A124773 1 1
%e A124773 2 2 1 1
%Y A124773 Cf. A066099, A124772, A124774, A011782 (row lengths), A000142 (row sums), A036039.
%K A124773 easy,nonn,tabf
%O A124773 0,5
%A A124773 _Franklin T. Adams-Watters_, Nov 06 2006