%I
%S 1,1,1,1,2,1,1,1,1,1,4,3,3,1,2,1,1,1,1,1,1,9,6,6,3,6,3,1,2,1,2,1,1,1,
%T 1,1,1,1,1,20,16,16,9,15,7,4,6,4,7,3,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,
%U 1,1,48,37,37,23,41,18,11,18,9,18,7,4,7,7,7,7,7,3,1,2,2,2,1,3,2,1,2,2,1,1,1
%N Triangle read by rows: T(n,k) is the number of endofunctions on n objects where the multiset of loop sizes forms the kth partition in Mathematica ordering.
%C The number of loops is equal to the number of components, but the sizes may be smaller.
%e For n = 3, the 7 endofunctions are (1,2,3) > (1,1,1), (1,1,2), (1,2,1), (2,1,1), (1,2,3), (1,3,2) and (2,3,1). The loops are respectively 1, 1, 12, 12, 123, 123 and 123, corresponding to partitions [1], [1], [1^2], [2], [1^3], [2,1] and [3]. The partitions of 1 to 3 in Mathematica order are [1], [2], [1^2], [3], [2,1] and [1^3], so row 3 is 2, 1,1, 1,1,1.
%e The triangle starts:
%e 1
%e 1, 1 1
%e 2, 1 1, 1 1 1
%e 4, 3 3, 1 2 1, 1 1 1 1 1
%K nonn,tabf
%O 1,5
%A _Franklin T. AdamsWatters_, Jan 05 2007
