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%I #7 May 08 2018 15:11:56
%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 Abramowitz and Stegun order).
%C After a(18) - for partition [1^5] - the sequence continues ?, 127, 687, 1611, 2102, 4031, 8589, ?, ?, ?, ?, ?, 255.
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%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, A122982, A122979, A036036, A074139.
%K more,nonn
%O 1,1
%A _Franklin T. Adams-Watters_, Sep 21 2006