OFFSET
0,5
COMMENTS
A hypergraph is uniform if all edges have the same size. The weight of a hypergraph is the sum of cardinalities of the edges. Weight is generally not the same as number of vertices.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
FORMULA
a(p) = 1 for prime p. - Andrew Howroyd, Jan 16 2024
EXAMPLE
Non-isomorphic representatives of the a(8) = 9 uniform connected hypergraphs:
{{1,2,3,4,5,6,7,8}}
{{1,2,3,7}, {4,5,6,7}}
{{1,2,5,6}, {3,4,5,6}}
{{1,3,4,5}, {2,3,4,5}}
{{1,2}, {1,3}, {2,4}, {3,4}}
{{1,3}, {2,4}, {3,5}, {4,5}}
{{1,4}, {2,3}, {2,4}, {3,4}}
{{1,4}, {2,5}, {3,5}, {4,5}}
{{1,5}, {2,5}, {3,5}, {4,5}}
PROG
(PARI) \\ See A331508 for T(n, k).
InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v, n, polcoef(p, n)), vector(#v, n, 1/n))}
a(n) = {if(n==0, 1, sumdiv(n, d, if(d==1 || d==n, d==1, InvEulerT(vector(d, i, T(n/d, i)))[d] )))} \\ Andrew Howroyd, Jan 16 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 20 2018
EXTENSIONS
a(11) onwards from Andrew Howroyd, Jan 16 2024
STATUS
approved