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%I #15 Mar 20 2013 15:09:36
%S 1,1,3,1,5,7,1,7,13,15,1,9,21,29,31,1,11,31,51,61,63,1,13,43,83,113,
%T 125,127,1,15,57,127,197,239,253,255,1,17,73,185,325,437,493,509,511,
%U 1,19,91,259,511,763,931,1003,1021,1023
%N Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with (right) waist exactly k.
%C Row sums are A221882.
%D A. D. Adeshola, V. Maltcev and A. Umar, Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain, (submitted 2013).
%F T(n,k) = 2*Sum_{p=1..k} C(n-1,p-1) - 1 for k >=1.
%e T(5,2) = 9 because there are exactly 9 order-preserving or order-reversing full contraction mappings (of a 5-chain) with (right) waist exactly 2, namely: (11112), (11122), (11222), (12222), (21111), (22111), (22211), (22221), (22222).
%Y Cf. A221876, A221877, A221878, A221879, A221880, A221882.
%K nonn,tabl
%O 1,3
%A _Abdullahi Umar_, Feb 28 2013
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