This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A184050 #9 Mar 31 2012 10:23:26 %S A184050 1,1,1,2,2,1,5,3,3,1,12,4,6,4,1,27,5,10,10,5,1,58,6,15,20,15,6,1,121, %T A184050 7,21,35,35,21,7,1 %N A184050 T(n,k) is the number of order-preserving and order-decreasing partial isometries (of an n-chain) with exactly k fixed points. %H A184050 R. Kehinde, S. O. Makanjuola and A. Umar, <a href="http://arxiv.org/abs/1101.2558">On the semigroup of order-decreasing partial isometries of a finite chain</a>, arXiv:1101.2558. %F A184050 T(n,0)= A000325(n-1) and T(n,k)=C(n,k), (k>0) %e A184050 T (4,2) = 6 because there are exactly 6 order-preserving and order-decreasing partial isometries (on a 4-chain) of fix 2, namely: (1,2)-->(1,2); (2,3)-->(2,3); (3,4)-->(3,4); (1,3)-->(1,3); (2,4)-->(2,4); (1,4)-->(1,4) - the mappings are coordinate-wise %Y A184050 Row sums are A000325 for n >= 0 %K A184050 nonn,tabl %O A184050 0,4 %A A184050 _Abdullahi Umar_, Jan 12 2011