A306018 - OEIS

%I #15 Feb 09 2020 20:14:45

%S 1,1,3,4,9,8,24,16,51,47,115,57,420,102,830,879,2962,298,15527,491,

%T 41275,80481,133292,1256,2038182,58671,2386862,24061887,23570088,4566,

%U 600731285,6843,1303320380,14138926716,1182784693,1820343112,542834549721,21638,31525806080

%N Number of non-isomorphic set multipartitions of weight n in which all parts have the same size.

%C A set multipartition of weight n is a finite multiset of finite nonempty sets whose cardinalities sum to n.

%C 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

%H Andrew Howroyd, <a href="/A306018/b306018.txt">Table of n, a(n) for n = 0..50</a>

%F a(p) = A000041(p) + 1 for prime p. - _Andrew Howroyd_, Sep 06 2018

%F a(n) = Sum_{d|n} A331461(n/d, d). - _Andrew Howroyd_, Feb 09 2020

%e Non-isomorphic representatives of the a(6) = 24 set multipartitions in which all parts have the same size:

%e {{1,2,3,4,5,6}}

%e {{1,2,3},{1,2,3}}

%e {{1,2,3},{4,5,6}}

%e {{1,2,5},{3,4,5}}

%e {{1,3,4},{2,3,4}}

%e {{1,2},{1,2},{1,2}}

%e {{1,2},{1,3},{2,3}}

%e {{1,2},{3,4},{3,4}}

%e {{1,2},{3,4},{5,6}}

%e {{1,2},{3,5},{4,5}}

%e {{1,3},{2,3},{2,3}}

%e {{1,3},{2,4},{3,4}}

%e {{1,4},{2,4},{3,4}}

%e {{1},{1},{1},{1},{1},{1}}

%e {{1},{1},{1},{2},{2},{2}}

%e {{1},{1},{2},{2},{2},{2}}

%e {{1},{1},{2},{2},{3},{3}}

%e {{1},{2},{2},{2},{2},{2}}

%e {{1},{2},{2},{3},{3},{3}}

%e {{1},{2},{3},{3},{3},{3}}

%e {{1},{2},{3},{3},{4},{4}}

%e {{1},{2},{3},{4},{4},{4}}

%e {{1},{2},{3},{4},{5},{5}}

%e {{1},{2},{3},{4},{5},{6}}

%o (PARI) \\ See A304942 for Blocks

%o a(n)={sumdiv(n, d, Blocks(n/d, n, d))} \\ _Andrew Howroyd_, Sep 05 2018

%Y Cf. A000005, A000041, A001315, A007716, A038041, A049311, A283877, A298422, A304942, A306017, A306019, A306020, A306021, A331461.

%K nonn

%O 0,3

%A _Gus Wiseman_, Jun 17 2018

%E Terms a(11) and beyond from _Andrew Howroyd_, Sep 05 2018