
EXAMPLE

The a(4) = 10 edgesets:
{{1,2,3,4}}
{{1,2},{3,4}}
{{1,3},{2,4}}
{{1,4},{2,3}}
{{1},{2},{3},{4}}
{{1,2},{1,3},{2,4},{3,4}}
{{1,2},{1,4},{2,3},{3,4}}
{{1,3},{1,4},{2,3},{2,4}}
{{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
{{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
Inequivalent representatives of the a(4) = 10 matrices:
[1 1 1 1]
.
[1 1 0 0] [1 0 1 0] [1 0 0 1]
[0 0 1 1] [0 1 0 1] [0 1 1 0]
.
[1 0 0 0] [1 1 0 0] [1 1 0 0] [1 0 1 0] [1 1 1 0]
[0 1 0 0] [1 0 1 0] [1 0 0 1] [1 0 0 1] [1 1 0 1]
[0 0 1 0] [0 1 0 1] [0 1 1 0] [0 1 1 0] [1 0 1 1]
[0 0 0 1] [0 0 1 1] [0 0 1 1] [0 1 0 1] [0 1 1 1]
.
[1 1 0 0]
[1 0 1 0]
[1 0 0 1]
[0 1 1 0]
[0 1 0 1]
[0 0 1 1]


MATHEMATICA

Table[Sum[SeriesCoefficient[Product[1+Times@@x/@s, {s, Subsets[Range[n], {m}]}], Sequence@@Table[{x[i], 0, k}, {i, n}]], {m, 0, n}, {k, 1, Binomial[n, m]}], {n, 5}]
