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.

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

Author

Omar E. Pol, Jan 10 2012

Keywords

• nonn
• tabl

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.

Examples

			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;
		

Links

• G. E. Andrews, The number of smallest parts in the partitions of n
• G. E. Andrews, F. G. Garvan, and J. Liang, Combinatorial interpretation of congruences for the spt-function
• Frank Garvan, Dyson's rank function and Andrews's SPT-function, slide 17.

Crossrefs

Cf. A092269, A195012, A195820.