A321677 -id:A321677 - cp's OEIS frontend

A369926 Number of non-isomorphic set multipartitions (multisets of sets) of weight n without endpoints or singletons.

1, 0, 0, 0, 1, 0, 3, 1, 9, 8, 34, 45, 177, 324, 1048, 2566, 8050, 22840, 73562, 231978, 780221, 2653042, 9377141, 33820014, 125473936, 475719042, 1846424607, 7317819857, 29611827086, 122190972442, 513900819816, 2201109101784, 9595815668795, 42553843201446, 191861748624324, 879049648551947

Offset: 0

Andrew Howroyd, Feb 06 2024

nonn

A singleton is a part of size 1. An endpoint is a vertex that appears in only one part.

a(n) is also the number of binary matrices with a total of n 1's and every row and column sum at least 2 up to permutation of rows and columns.

			The a(8) = 9 matrices are:
   [1 1 1 1]  [1 1 1]  [1 1 1 0]  [1 1 1 1]
   [1 1 1 1]  [1 1 1]  [1 1 0 1]  [1 1 0 0]
              [1 1 0]  [0 0 1 1]  [0 0 1 1]
.
   [1 1]  [1 1 0]  [1 1 0]  [1 1 0 0]  [1 1 0 0]
   [1 1]  [1 1 0]  [1 1 0]  [1 1 0 0]  [1 0 1 0]
   [1 1]  [1 0 1]  [1 0 1]  [0 0 1 1]  [0 1 0 1]
   [1 1]  [1 0 1]  [0 1 1]  [0 0 1 1]  [0 0 1 1]

Andrew Howroyd, Table of n, a(n) for n = 0..50

Row sums of A369927.
A321677 is the case without singletons but allowing endpoints (or by duality without endpoints but allowing singletons).
Cf. A330055 (set-systems).

PARI
```
Vec(G(25,1)) \\ G defined in A369927.
```

cp's OEIS Frontend

A369926 Number of non-isomorphic set multipartitions (multisets of sets) of weight n without endpoints or singletons.

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