cp's OEIS Frontend

A302129 Number of unlabeled uniform connected hypergraphs of weight n.

%I A302129 #14 Jan 16 2024 22:05:01
%S A302129 1,1,1,1,2,1,6,1,9,10,17,1,108,1,86,401,482,1,4469,1,8435,47959,8082,
%T A302129 1,1007342,52414,112835,15338453,11899367,1,362657533,1,977129970,
%U A302129 9349593479,35787684,1771297657,390347162497,1,779945988,9360467497257,16838238535445
%N A302129 Number of unlabeled uniform connected hypergraphs of weight n.
%C A302129 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.
%H A302129 Andrew Howroyd, <a href="/A302129/b302129.txt">Table of n, a(n) for n = 0..50</a>
%F A302129 a(p) = 1 for prime p. - _Andrew Howroyd_, Jan 16 2024
%e A302129 Non-isomorphic representatives of the a(8) = 9 uniform connected hypergraphs:
%e A302129   {{1,2,3,4,5,6,7,8}}
%e A302129   {{1,2,3,7}, {4,5,6,7}}
%e A302129   {{1,2,5,6}, {3,4,5,6}}
%e A302129   {{1,3,4,5}, {2,3,4,5}}
%e A302129   {{1,2}, {1,3}, {2,4}, {3,4}}
%e A302129   {{1,3}, {2,4}, {3,5}, {4,5}}
%e A302129   {{1,4}, {2,3}, {2,4}, {3,4}}
%e A302129   {{1,4}, {2,5}, {3,5}, {4,5}}
%e A302129   {{1,5}, {2,5}, {3,5}, {4,5}}
%o A302129 (PARI) \\ See A331508 for T(n, k).
%o A302129 InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v,n,polcoef(p,n)), vector(#v,n,1/n))}
%o A302129 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
%Y A302129 Cf. A000005, A007716, A038041, A038041, A048143, A299353, A301481, A301920, A301924, A306019, A306021, A331508.
%K A302129 nonn
%O A302129 0,5
%A A302129 _Gus Wiseman_, Jun 20 2018
%E A302129 a(11) onwards from _Andrew Howroyd_, Jan 16 2024