%I A151359
%S A151359 0,1,1,1,1,1,1,0,0,1,3,7,15,31,63,119,210,336,462,462,0,0,0,1,6,25,
%T A151359 90,301,966,2989,8925,25641,70455,183183,441441,966966,1849848,
%U A151359 2858856,2858856,0,0,0,0,1,10,65,350,1701,7770,33985,143605,588511
%N A151359 Triangle read by rows: T(n,k) = number of partitions of [1..k] into n 
               nonempty clumps of sizes 1, 2, 3, 4, 5 or 6 (n >= 0, 0 <= k <= 6n).
%C A151359 Row n has 6n+1 entries.
%H A151359 David Applegate and N. J. A. Sloane, <a href="http://arxiv.org/abs/0907.0513">
               The Gift Exchange Problem</a> (arXiv:0907.0513, 2009)
%e A151359 Triangle begins:
%e A151359 [0, 1, 1, 1, 1, 1, 1]
%e A151359 [0, 0, 1, 3, 7, 15, 31, 63, 119, 210, 336, 462, 462]
%e A151359 [0, 0, 0, 1, 6, 25, 90, 301, 966, 2989, 8925, 25641, 70455, 183183, 441441, 
               966966, 1849848, 2858856, 2858856]
%e A151359 [0, 0, 0, 0, 1, 10, 65, 350, 1701, 7770, 33985, 143605, 588511, 2341339, 
               9032023, 33668635, 120681561, 413104692, 1337944608, 4046710668, 
               11216721516, 27756632904, 58555088592, 96197645544, 96197645544]
%e A151359 [0, 0, 0, 0, 0, 1, 15, 140, 1050, 6951, 42525, 246400, 1370985, 7383376, 
               38657619, 197212015, 980839860, 4752728981, 22399494117, 102410296989, 
               452572985865, 1924000439361, 7820764020069, 30157961878044, 109184327692440, 
               365935843649376, 1113006758944080, 2982608000091720, 6696799094545560, 
               11423951396577720, 11423951396577720]
%e A151359 ...
%Y A151359 This is one of a sequence of triangles: A144331, A144385, A144643, A151338, 
               A151359, ...
%Y A151359 See A151511, A151512 for other versions.
%Y A151359 Sequence in context: A006739 A119407 A043734 this_sequence A147596 A115567 
               A043740
%Y A151359 Adjacent sequences: A151356 A151357 A151358 this_sequence A151360 A151361 
               A151362
%K A151359 nonn,tabf
%O A151359 0,11
%A A151359 N. J. A. Sloane (njas(AT)research.att.com), May 14 2009