A330368 Irregular triangle read by rows in which row n lists the ranks of the partitions of n in nonincreasing order.

0, 1, -1, 2, 0, -2, 3, 1, 0, -1, -3, 4, 2, 1, 0, -1, -2, -4, 5, 3, 2, 1, 1, 0, -1, -1, -2, -3, -5, 6, 4, 3, 2, 2, 1, 0, 0, 0, -1, -2, -2, -3, -4, -6, 7, 5, 4, 3, 3, 2, 2, 1, 1, 1, 0, 0, -1, -1, -1, -2, -2, -3, -3, -4, -5, -7, 8, 6, 5, 4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -2, -2, -2, -3, -3, -4, -4, -5, -6, -8

Offset: 1

Author

Omar E. Pol, Dec 12 2019

Keywords

• sign
• tabf

Comments

The rank of a partition is the largest part minus the number of parts.

For more about this ordering, see A330370.

First differs from A105805 at a(49) = T(7,5).

Examples

			Triangle begins:
                              0;
                            1, -1;
                          2,  0, -2;
                      3,  1,  0, -1, -3;
                  4,  2,  1,  0, -1, -2, -4;
          5,  3,  2,  1,  1,  0, -1, -1, -2, -3, -5;
  6,  4,  3,  2,  2,  1,  0,  0,  0, -1, -2, -2, -3, -4, -6;
...
		

Crossrefs

Row n has length A000041(n).

Row sums give A000004.

Cf. A105805, A105806, A194547, A194549, A195822, A208478, A209616, A330370.

Extensions

Edited by N. J. A. Sloane, Sep 15 2020