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%I #5 Mar 30 2012 17:35:16
%S 3,7,12,15,37,73,31,103,146,319,731,63,271,505,1191,1833,4618
%N Number of distributive sublattices of the lattice of k-tuples less than the n-th partition (in Mathematica order).
%C After a(18) - for partition [1^5] - the sequence continues ?, 127, 687, 1611, 4031, 2102, 8589, ?, ?, ?, ?, ?, 255.
%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. A122978, A122981, A122980, A080577, A074139.
%K more,nonn
%O 1,1
%A _Franklin T. Adams-Watters_, Sep 21 2006