OFFSET
0,5
COMMENTS
T(n,k) is the number of Green's H-classes contained in the D-class of rank k in the full transformation semigroup on [n]. - Geoffrey Critzer, Dec 27 2022
REFERENCES
O. Ganyushkin and V. Mazorchuk, Classical Finite Transformation Semigroups, Springer, 2009, pages 58-62.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..230
Wikipedia, Green's relations
Wikipedia, Transformation semigroup
FORMULA
EXAMPLE
Triangle begins:
1;
0, 1;
0, 2, 1;
0, 3, 9, 1;
0, 4, 42, 24, 1;
...
MATHEMATICA
Flatten[Table[Table[Binomial[n, k] StirlingS2[n, k], {k, 0, n}], {n, 0, 10}], 1]
PROG
(Maxima) create_list(binomial(n, k)*stirling2(n, k), n, 0, 12, k, 0, n); /* Emanuele Munarini, Mar 11 2011 */
CROSSREFS
KEYWORD
AUTHOR
Philippe Deléham, Dec 18 2003
EXTENSIONS
Edited by Olivier Gérard, Oct 23 2012
STATUS
approved