A321256 Regular triangle where T(n,k) is the number of non-isomorphic connected set systems of weight n with density -1 <= k <= n-2.

1, 1, 0, 2, 0, 0, 4, 0, 0, 0, 6, 1, 0, 0, 0, 13, 5, 0, 0, 0, 0, 23, 12, 2, 0, 0, 0, 0, 49, 36, 11, 0, 0, 0, 0, 0, 100, 95, 39, 5, 0, 0, 0, 0, 0, 220, 262, 143, 32, 1, 0, 0, 0, 0, 0

Offset: 1

Author

Gus Wiseman, Nov 01 2018

Keywords

• nonn
• tabl
• more

Comments

A set system is a finite set of finite nonempty sets. The density of a set system is the sum of sizes of each part (weight) minus the number of parts minus the number of vertices.

Examples

			Triangle begins:
    1
    1   0
    2   0   0
    4   0   0   0
    6   1   0   0   0
   13   5   0   0   0   0
   23  12   2   0   0   0   0
   49  36  11   0   0   0   0   0
  100  95  39   5   0   0   0   0   0
  220 262 143  32   1   0   0   0   0   0
		

Crossrefs

First column is A321228. Row sums are A007718.

Cf. A007716, A030019, A056156, A283877, A293607, A300913, A319557, A321155, A321253, A321254.