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A127125 Triangle read by rows: T(n,k) is the number of endofunctions on n objects where the multiset of loop sizes forms the k-th partition in Mathematica ordering. 1

%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 k-th 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, 1|2, 12, 1|2|3, 1|23 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. Adams-Watters_, Jan 05 2007

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Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)