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 A257493. Burnside's lemma can be used to extend this method to the unlabeled case.
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 2 3 3 4 4 ...
3 | 1 1 3 5 9 13 22 30 ...
4 | 1 1 5 12 43 106 321 787 ...
5 | 1 1 7 31 264 1856 12703 71457 ...
6 | 1 1 11 103 2804 65481 1217727 16925049 ...
7 | 1 1 15 383 44524 3925518 224549073 8597641912 ...
...
CROSSREFS
Main diagonal is A333734.
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 04 2020
STATUS
approved