OFFSET
0,13
COMMENTS
Terms may be computed without generating each matrix by enumerating the number of matrices by column sum sequence using dynamic programming. A PARI program showing this technique for the labeled case is given in A376935. Burnside's lemma can be used to extend this method to the unlabeled case. This seems to require looping over partitions for both rows and columns.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..119 (first 15 antidiagonals)
FORMULA
T(n,k) = T(k,n).
EXAMPLE
Array begins:
============================================================================
n\k | 0 1 2 3 4 5 6 7 ...
----+-----------------------------------------------------------------------
0 | 1 1 1 1 1 1 1 1 ...
1 | 1 1 1 1 1 1 1 1 ...
2 | 1 1 2 3 4 5 7 8 ...
3 | 1 1 3 7 19 46 132 345 ...
4 | 1 1 4 19 194 3144 65548 1272696 ...
5 | 1 1 5 46 3144 601055 128665248 24124134235 ...
6 | 1 1 7 132 65548 128665248 294494683312 607662931576945 ...
7 | 1 1 8 345 1272696 24124134235 607662931576945 14584161564179926207 ...
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Oct 12 2024
STATUS
approved