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%I #19 Mar 20 2013 13:43:25
%S 1,2,2,3,8,2,4,18,12,2,5,32,36,16,2,6,50,80,60,20,2,7,72,150,160,90,
%T 24,2,8,98,252,350,280,126,28,2,9,128,392,672,700,448,168,32,2,10,162,
%U 576,1176,1512,1260,672,216,36,2
%N Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with height 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).
%F T(n,1) = n and T(n,k) = 2(n-k+1)*C(n-1,k-1) if k > 1.
%e T (3,2) = 8 because there are exactly 8 order-preserving full contraction mappings (of a 3-chain) with exactly height 2, namely: (112), (122), (211), (221), (223), (233), (322), (332).
%Y Cf. A221876, A221878, A221879, A221880, A221881, A221882.
%K nonn
%O 1,2
%A _Abdullahi Umar_, Feb 28 2013