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A195011
Triangle read by rows: T(n,m) = number of vector partitions of n in S with crank m counted according to the weight w_1.
4
1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2, 2, 1, 1, 0, 4, 4, 3, 2, 1, 1, 0, 5, 4, 4, 3, 2, 1, 1, 0, 7, 7, 6, 5, 3, 2, 1, 1, 0, 10, 9, 8, 6, 5, 3, 2, 1, 1, 0, 13, 13, 11, 10, 7, 5, 3, 2, 1, 1, 0, 17, 16, 15, 12, 10, 7, 5, 3, 2, 1, 1
OFFSET
0,11
COMMENTS
This is the essential triangle in the square array of the Andrews-Garvan-Liang paper, see chapter 7 and page 3 for a precise definition.
Apparently columns (their positive terms) converge to A000041.
EXAMPLE
Triangle begins:
1;
1, 0;
1, 1, 0;
1, 1, 1, 0;
2, 2, 1, 1, 0;
2, 2, 2, 1, 1, 0;
4, 4, 3, 2, 1, 1, 0;
5, 4, 4, 3, 2, 1, 1, 0;
7, 7, 6, 5, 3, 2, 1, 1, 0;
10,9, 8, 6, 5, 3, 2, 1, 1, 0;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Jan 10 2012
STATUS
approved