

A144066


T(n, k) is the number of orderpreserving partial transformations (of an nelement chain) of height k (height(alpha) = Im(alpha)).


0



1, 1, 1, 1, 6, 1, 1, 21, 15, 1, 1, 60, 102, 28, 1, 1, 155, 490, 310, 45, 1, 1, 378, 1935, 2220, 735, 66, 1, 1, 889, 6741, 12285, 7315, 1491, 91, 1
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OFFSET

0,5


COMMENTS

T(n, k) is also the number of elements in the Green's Jclasses of the monoid of orderpreserving partial transformations (of an nelement chain). Sum of rows of T(n, k) is A123164.


LINKS

Table of n, a(n) for n=0..35.
Laradji, A. and Umar, A. Combinatorial results for semigroups of orderpreserving partial transformations, Journal of Algebra 278, (2004), 342359.
Laradji, A. and Umar, A. Combinatorial results for semigroups of orderdecreasing partial transformations, J. Integer Seq. 7 (2004), 04.3.8


FORMULA

J(n,k)=C(n,k)*A112857(n,k); C(n1,k1)*J(n,k)=2((nk+1)/(nk))J(n1,k)
+ C(n,k)J(n1,k1)


EXAMPLE

J(2,1) = 6 because there are exactly 6 orderpreserving partial transformations (on a 2element chain)of height 1, namely: (1)>(1), (1)>(2), (2)>(1), (2)>(2), (1,2)>(1,1),(1,2)>(2,2) the mappings are coordinatewise.


CROSSREFS

A123164, A112857
Sequence in context: A146988 A203954 A060972 * A296827 A056941 A157638
Adjacent sequences: A144063 A144064 A144065 * A144067 A144068 A144069


KEYWORD

nonn,tabl


AUTHOR

Abdullahi Umar, Sep 09 2008


STATUS

approved



