OFFSET
0,8
COMMENTS
A(n,k) is the number of non-isomorphic set multipartitions (multiset of sets) with k parts each part has size n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..152
FORMULA
A306018(n) = Sum_{d|n} A(n/d, d).
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 2 3 5 7 11 15 ...
2 | 1 1 3 8 23 66 212 686 ...
3 | 1 1 4 16 93 652 6369 79568 ...
4 | 1 1 5 30 332 6414 226041 12848128 ...
5 | 1 1 6 50 1062 56712 7295812 1817321457 ...
6 | 1 1 7 80 3117 441881 195486906 200065951078 ...
7 | 1 1 8 120 8399 3006771 4298181107 17131523059493 ...
...
The A(2,3) = 8 matrices are:
[1 0 0] [1 1 0] [1 1 1] [1 1 0] [1 1 0] [1 1 1] [1 1 0] [1 1 1]
[1 0 0] [1 0 0] [1 0 0] [1 1 0] [1 0 1] [1 1 0] [1 0 1] [1 1 1]
[0 1 0] [0 1 0] [0 1 0] [0 0 1] [0 1 0] [0 0 1] [0 1 1]
[0 1 0] [0 0 1] [0 0 1] [0 0 1] [0 0 1]
[0 0 1] [0 0 1]
[0 0 1]
PROG
(PARI) \\ See A304942 for Blocks
T(n, k)={Blocks(k, n*k, n)}
{ for(n=0, 7, for(k=0, 6, print1(T(n, k), ", ")); print) }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jan 18 2020
STATUS
approved