A318398
Number of triples of set partitions of {1,2,...,n} whose meet is {{1},{2},...,{n}}.
Original entry on oeis.org
1, 7, 103, 2707, 110857, 6517129, 521167549, 54510591469, 7235648605909, 1190181847444189, 237953165658759679, 56905537750421669449, 16059682765076576965879, 5287171379685771887014489, 2010360123437921314268936809, 875173620070717892287441139989
Offset: 1
The a(2) = 7 triples:
{{1},{2}} {{1},{2}} {{1},{2}}
{{1},{2}} {{1},{2}} {{1,2}}
{{1},{2}} {{1,2}} {{1},{2}}
{{1},{2}} {{1,2}} {{1,2}}
{{1,2}} {{1},{2}} {{1},{2}}
{{1,2}} {{1},{2}} {{1,2}}
{{1,2}} {{1,2}} {{1},{2}}
Cf.
A000110,
A000258,
A001247,
A008277,
A048994,
A059849,
A060639,
A181939,
A318389,
A318391,
A318393,
A318399.
-
Table[Sum[StirlingS1[n,k]*BellB[k]^3,{k,0,n}],{n,10}]
A318815
Number of triples of set partitions of {1,2,...,n} whose join is {{1,2,...,n}}.
Original entry on oeis.org
1, 7, 103, 2773, 117697, 7167619, 590978941, 63385879261, 8584707943381, 1434654097736101, 290409845948305321, 70125579500764771585, 19940633217840575968969, 6603748351832744611210549, 2522614472277243822293033719, 1102166886808604068546379343289
Offset: 1
The a(2) = 7 triples:
{{1},{2}} {{1},{2}} {{1,2}}
{{1},{2}} {{1,2}} {{1},{2}}
{{1},{2}} {{1,2}} {{1,2}}
{{1,2}} {{1},{2}} {{1},{2}}
{{1,2}} {{1},{2}} {{1,2}}
{{1,2}} {{1,2}} {{1},{2}}
{{1,2}} {{1,2}} {{1,2}}
Cf.
A000110,
A000258,
A001247,
A008277,
A048994,
A059849,
A060639,
A181939,
A318389,
A318391,
A318393,
A318398,
A318399.
-
nn=10;Table[n!*SeriesCoefficient[Log[1+Sum[BellB[n]^3*x^n/n!,{n,nn}]],{x,0,n}],{n,nn}]
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.
Original entry on oeis.org
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
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}}}
Cf.
A007716,
A050336,
A050338,
A255906,
A269134,
A317533,
A317791,
A318393,
A318399,
A318564,
A318565,
A318566.
Showing 1-3 of 3 results.