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A249620
Triangle read by rows: T(m,n) = number of partitions of the multiset with m elements and signature corresponding to n-th integer partition (A194602).
6
1, 1, 2, 2, 5, 4, 3, 15, 11, 7, 9, 5, 52, 36, 21, 26, 12, 16, 7, 203, 135, 74, 92, 38, 52, 19, 66, 29, 31, 11, 877, 566, 296, 371, 141, 198, 64, 249, 98, 109, 30, 137, 47, 57, 15, 4140, 2610, 1315, 1663, 592, 850, 250, 1075, 392, 444, 105, 560
OFFSET
0,3
COMMENTS
This triangle shows the same numbers in each row as A129306 and A096443, but in this arrangement the multisets in column n correspond to the n-th integer partition in the infinite order defined by A194602.
Row lengths: A000041 (partition numbers), Row sums: A035310
Columns: 0: A000110 (Bell), 1: A035098 (near-Bell), 2: A169587, 4: A169588
Last in row: end-1: A091437, end: A000041 (partition numbers)
The rightmost columns form a reflected version of the triangle A126442:
n 0 1 2 4 6 10 14 21 (A000041(1,2,3...)-1)
m
1 1
2 2 2
3 5 4 3
4 15 11 7 5
5 52 36 21 12 7
6 203 135 74 38 19 11
7 877 566 296 141 64 30 15
8 4140 2610 1315 592 250 105 45 22
A249619 shows the number of permutations of the same multisets.
EXAMPLE
See "The T(5,2)=21 partitions of {1,1,1,2,3}" link. Similar links for m=1..8 are in "Partitions of multisets" (Wikiversity).
Triangle begins:
n 0 1 2 3 4 5 6 7 8 9 10
m
0 1
1 1
2 2 2
3 5 4 3
4 15 11 7 9 5
5 52 36 21 26 12 16 7
6 203 135 74 92 38 52 19 66 29 31 11
KEYWORD
nonn,tabf
AUTHOR
Tilman Piesk, Nov 04 2014
STATUS
approved