
EXAMPLE

Nonisomorphic representatives of the a(3) = 8 uniform hypergraphs on 3 unlabeled nodes with at least one hyperedge: {{}}, {1}, {1,2}, {1,2,3}, {12}, {12,13}, {12,13,23}, {123}.


MAPLE

g:= (l, i, n)> `if`(i=0, `if`(n=0, [[]], []), [seq(map(x>
[x[], j], g(l, i1, nj))[], j=0..min(l[i], n))]):
h:= (p, v)> (q> add((s> add(`if`(andmap(i> irem(k[i], p[i]
/igcd(t, p[i]))=0, [$1..q]), mul((m> binomial(m, k[i]*m
/p[i]))(igcd(t, p[i])), i=1..q), 0), t=1..s)/s)(ilcm(seq(
`if`(k[i]=0, 1, p[i]), i=1..q))), k=g(p, q, v)))(nops(p)):
b:= (n, i, l, v)> `if`(n=0 or i=1, 2^((p> h(p, v))([l[], 1$n]))
/n!, add(b(ni*j, i1, [l[], i$j], v)/j!/i^j, j=0..n/i)):
T:= proc(n, k) T(n, k):=`if`(k>nk, T(n, nk), b(n$2, [], k)) end:
a:= n> add(T(n, k)1, k=0..n):
seq(a(n), n=0..10);
