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.
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.
LINKS
Tilman Piesk, Triangle rows m=0..8, flattened.
Tilman Piesk, Partitions of multisets (Wikiversity)
Tilman Piesk, The T(5,2)=21 partitions of {1,1,1,2,3}
Tilman Piesk, PHP code used to calculate the examples
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
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Tilman Piesk, Nov 04 2014
STATUS
approved