|
| |
|
|
A113547
|
|
Triangle read by rows: number of labeled partitions of n with maximin m.
|
|
0
| |
|
|
1, 1, 1, 1, 2, 2, 1, 4, 5, 5, 1, 8, 13, 15, 15, 1, 16, 35, 47, 52, 52, 1, 32, 97, 153, 188, 203, 203, 1, 64, 275, 515, 706, 825, 877, 877, 1, 128, 793, 1785, 2744, 3479, 3937, 4140, 4140, 1, 256, 2315, 6347, 11002, 15177, 18313, 20270, 21147, 21147, 1, 512, 6817
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
COMMENTS
| The maximin of a partition is the maximum over all parts of the minimum label in each part. If the rows are reversed, the result is the number of partitions of n with minimax m.
|
|
|
FORMULA
| T(n, m)=Sum_{k=1..m} S2(m-1, k-1)*k^(n-m), where S2 is the Stirling numbers of the second kind (A08277). T(n, n)=T(n, n-1)=B(n-1), where B is the Bell numbers (A000110). T(n, n-2)=B(n-1)-B(n-3).
|
|
|
EXAMPLE
| Maximin [123]=max(1)=1, maximin [12|3]=max(1,3)=3, maximin [13|2]=max(1,2)=2, maximin [1|23]=max(1,2)=2 and maximin [1|2|3]=max(1,2,3)=3, so for n=3 the multiset of maximins is {1,2,2,3,3}, making the 3rd line 1,2,2.
|
|
|
CROSSREFS
| Cf. A008277, A000110.
Sequence in context: A064189 A063415 A098977 * A115313 A048942 A121484
Adjacent sequences: A113544 A113545 A113546 * A113548 A113549 A113550
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 2006
|
| |
|
|
