OFFSET
0,1
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..14, flattened
Jianguo Qian, Enumeration of unlabeled uniform hypergraphs, Discrete Math. 326 (2014), 66--74. MR3188989.
Wikipedia, Hypergraph
FORMULA
T(n,k) = T(n,n-k) for 0 <= k <= n.
EXAMPLE
Triangle T(n,k) begins:
2;
2, 2;
2, 3, 2;
2, 4, 4, 2;
2, 5, 11, 5, 2;
2, 6, 34, 34, 6, 2;
2, 7, 156, 2136, 156, 7, 2;
2, 8, 1044, 7013320, 7013320, 1044, 8, 2;
...
MAPLE
g:= (l, i, n)-> `if`(i=0, `if`(n=0, [[]], []), [seq(map(x->
[x[], j], g(l, i-1, n-j))[], 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(n-i*j, i-1, [l[], i$j], v)/j!/i^j, j=0..n/i)):
T:= proc(n, k) option remember; `if`(k>n-k,
T(n, n-k), b(n$2, [], k))
end:
seq(seq(T(n, k), k=0..n), n=0..9);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Aug 20 2019
STATUS
approved