OFFSET
1,5
COMMENTS
T(n,k) is the number of permutations in S_n with Ulam distance from the identity equal to k.
Mirror image of triangle in A047874.
REFERENCES
P. Diaconis, Group Representations in Probability and Statistics, IMS, 1988; see p. 112.
See A047874 for further references, etc.
LINKS
Alois P. Heinz, Rows n = 1..60, flattened
E. Irurozki, Sampling and learning distance-based probability models for permutation spaces, PhD Dissertation, Department of Computer Science and Artificial Intelligence of the University of the Basque Country, 2015.
E. Irurozki, B. Calvo, J. Ceberio, and J. A. Lozano, Mallows model under the Ulam distance: a feasible combinatorial approach, 2014.
Ekhine Irurozki, B. Calvo, J. A. Lozano, PerMallows: An R Package for Mallows and Generalized Mallows Models, Journal of Statistical Software, August 2016, Volume 71, Issue 12. doi: 10.18637/jss.v071.i12
EXAMPLE
Triangle T(n,k) begins:
1;
1, 1;
1, 4, 1;
1, 13, 9, 1;
1, 41, 61, 16, 1;
1, 131, 381, 181, 25, 1;
1, 428, 2332, 1821, 421, 36, 1;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Mar 01 2007
STATUS
approved