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A330368
Irregular triangle read by rows in which row n lists the ranks of the partitions of n in nonincreasing order.
5
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
1,4
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).
EXAMPLE
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.
Sequence in context: A089596 A319876 A105805 * A194547 A257570 A220417
KEYWORD
sign,tabf
AUTHOR
Omar E. Pol, Dec 12 2019
EXTENSIONS
Edited by N. J. A. Sloane, Sep 15 2020
STATUS
approved