|
|
A362925
|
|
Triangle read by rows: T(n,m), n >= 0, 0 <= m <= n, is number of partitions of the set {1,2,...,n} that have at most one block contained in {1,...,m}.
|
|
4
|
|
|
1, 1, 1, 2, 2, 1, 5, 5, 4, 1, 15, 15, 13, 8, 1, 52, 52, 47, 35, 16, 1, 203, 203, 188, 153, 97, 32, 1, 877, 877, 825, 706, 515, 275, 64, 1, 4140, 4140, 3937, 3479, 2744, 1785, 793, 128, 1, 21147, 21147, 20270, 18313, 15177, 11002, 6347, 2315, 256, 1, 115975, 115975, 111835, 102678, 88033, 68303, 45368, 23073, 6817, 512, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
A variant of A113547 and A362924. See those entries for further information.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
Triangle begins:
1;
1, 1;
2, 2, 1;
5, 5, 4, 1;
15, 15, 13, 8, 1;
52, 52, 47, 35, 16, 1;
203, 203, 188, 153, 97, 32, 1;
877, 877, 825, 706, 515, 275, 64, 1;
4140, 4140, 3937, 3479, 2744, 1785, 793, 128, 1;
21147, 21147, 20270, 18313, 15177, 11002, 6347, 2315, 256, 1;
115975, 115975, 111835, 102678, 88033, 68303, 45368, 23073, 6817, 512, 1;
...
|
|
MAPLE
|
T:= (n, k)-> add(Stirling2(n-k, j)*(j+1)^k, j=0..n-k):
|
|
MATHEMATICA
|
A362925[n_, m_]:=Sum[StirlingS2[n-m, k](k+1)^m, {k, 0, n-m}];
|
|
CROSSREFS
|
Column k=2 gives A078468(n-2) for n>=2.
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|