A318816 Regular tetrangle where T(n,k,i) is the number of non-isomorphic multiset partitions of length i of multiset partitions of length k of multisets of size n.

1, 2, 2, 2, 3, 4, 4, 3, 4, 3, 5, 14, 14, 9, 20, 9, 5, 14, 9, 5, 7, 28, 28, 33, 80, 33, 16, 68, 52, 16, 7, 28, 33, 16, 7, 11, 69, 69, 104, 266, 104, 74, 356, 282, 74, 29, 199, 253, 118, 29, 11, 69, 104, 74, 29, 11, 15, 134, 134, 294, 800, 294, 263, 1427, 1164

Offset

1,2

Links

Table of n, a(n) for n=1..65.

Example

Tetrangle begins:
  1   2     3        5             7
      2 2   4 4     14 14         28 28
            3 4 3    9 20  9      33 80 33
                     5 14  9  5   16 68 52 16
                                   7 28 33 16  7
Non-isomorphic representatives of the T(4,3,2) = 20 multiset partitions:
  {{{1}},{{1},{1,1}}}  {{{1,1}},{{1},{1}}}
  {{{1}},{{1},{1,2}}}  {{{1,1}},{{1},{2}}}
  {{{1}},{{1},{2,2}}}  {{{1,1}},{{2},{2}}}
  {{{1}},{{1},{2,3}}}  {{{1,1}},{{2},{3}}}
  {{{1}},{{2},{1,1}}}  {{{1,2}},{{1},{1}}}
  {{{1}},{{2},{1,2}}}  {{{1,2}},{{1},{2}}}
  {{{1}},{{2},{1,3}}}  {{{1,2}},{{1},{3}}}
  {{{1}},{{2},{3,4}}}  {{{1,2}},{{3},{4}}}
  {{{2}},{{1},{1,1}}}  {{{2,3}},{{1},{1}}}
  {{{2}},{{1},{1,3}}}
  {{{2}},{{3},{1,1}}}

Crossrefs

Cf. A007716, A050336, A050338, A255906, A269134, A317533, A317791, A318393, A318399, A318564, A318565, A318566.

Sequence in context: A341121 A144000 A306284 * A085202 A096009 A000224

Adjacent sequences: A318813 A318814 A318815 * A318817 A318818 A318819

Keyword

nonn,tabf

Author

Gus Wiseman, Sep 04 2018

Status

approved