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Triangle read by rows: T(n,k) (2 <= k <= n) = dimension of partially ordered set of all 1-element and (k-1)-element subsets of an n-set.
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%I #7 Jan 17 2013 11:12:23

%S 2,2,3,2,3,4,2,4,4,5,2,4,5,5,6,2,4,6,6,6,7,2,4,6,7,7,7,8,2,4,6,8,8,8,

%T 8,9,2,4,6,8,9,9,9,9,10,2,4,7,9,10,10,10,10,10,11,2,4,7,9,10,11,11,11,

%U 11,11,12,2,5,7,9,11,12,12,12,12,12,12,13,2,5,7,9,12,12,13,13,13,13,13,13,14

%N Triangle read by rows: T(n,k) (2 <= k <= n) = dimension of partially ordered set of all 1-element and (k-1)-element subsets of an n-set.

%D Trotter, William T., Jr. Some combinatorial problems for permutations. Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1977), pp. 619--632. Congressus Numerantium, No. XIX, Utilitas Math., Winnipeg, Man., 1977. MR0480110 (58 #309).

%e Triangle begins:

%e 2

%e 2 3

%e 2 3 4

%e 2 4 4 5

%e 2 4 5 5 6

%e 2 4 6 6 6 7

%e 2 4 6 7 7 7 8

%e 2 4 6 8 8 8 8 9

%e 2 4 6 8 9 9 9 9 10

%e 2 4 7 9 10 10 10 10 10 11

%e 2 4 7 9 10 11 11 11 11 11 12

%e 2 5 7 9 11 12 12 12 12 12 12 13

%e 2 5 7 9 12 12 13 13 13 13 13 13 14...

%K nonn,tabl

%O 2,1

%A _N. J. A. Sloane_, Apr 03 2012