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%I #7 Mar 14 2016 03:32:39
%S 2,4,7,8,21,45,16,58,84,200,500,32,152,293,748,1184,3220
%N Number of distributive sublattices of the lattice of k-tuples less than the n-th partition (in Mathematica order), that include the maximum element.
%C After a(18) - for partition [1^5] - the sequence continues ?, 64, 384, 938, 2520, 1238, 5591, ?, ?, ?, ?, ?, 128.
%e For a(5), partition [2,1], the lattice consists of the 6 pairs (i,j) where 0<=i<=2 and 0<=j<=1, with (i,j) <= (i',j') iff i<=i' and j<=j'. {(2,1), (2,0), (0,1), (0,0)} is one distributive sublattice.
%Y Cf. A122977, A122979, A122982, A080577, A074139.
%K nonn,more
%O 1,1
%A _Franklin T. Adams-Watters_, Sep 21 2006