OFFSET
0,3
COMMENTS
A set multipartition of weight n is a finite multiset of finite nonempty sets whose cardinalities sum to n.
Number of distinct binary matrices with all row sums equal and total sum n, up to row and column permutations. - Andrew Howroyd, Sep 05 2018
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
FORMULA
a(p) = A000041(p) + 1 for prime p. - Andrew Howroyd, Sep 06 2018
a(n) = Sum_{d|n} A331461(n/d, d). - Andrew Howroyd, Feb 09 2020
EXAMPLE
Non-isomorphic representatives of the a(6) = 24 set multipartitions in which all parts have the same size:
{{1,2,3,4,5,6}}
{{1,2,3},{1,2,3}}
{{1,2,3},{4,5,6}}
{{1,2,5},{3,4,5}}
{{1,3,4},{2,3,4}}
{{1,2},{1,2},{1,2}}
{{1,2},{1,3},{2,3}}
{{1,2},{3,4},{3,4}}
{{1,2},{3,4},{5,6}}
{{1,2},{3,5},{4,5}}
{{1,3},{2,3},{2,3}}
{{1,3},{2,4},{3,4}}
{{1,4},{2,4},{3,4}}
{{1},{1},{1},{1},{1},{1}}
{{1},{1},{1},{2},{2},{2}}
{{1},{1},{2},{2},{2},{2}}
{{1},{1},{2},{2},{3},{3}}
{{1},{2},{2},{2},{2},{2}}
{{1},{2},{2},{3},{3},{3}}
{{1},{2},{3},{3},{3},{3}}
{{1},{2},{3},{3},{4},{4}}
{{1},{2},{3},{4},{4},{4}}
{{1},{2},{3},{4},{5},{5}}
{{1},{2},{3},{4},{5},{6}}
PROG
(PARI) \\ See A304942 for Blocks
a(n)={sumdiv(n, d, Blocks(n/d, n, d))} \\ Andrew Howroyd, Sep 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 17 2018
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Sep 05 2018
STATUS
approved