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A371830 Irregular triangle read by rows: T(n,k) is the number of unlabeled n-vertex hypergraphs (or set systems) with k hyperedges (none of which is empty), 0 <= k <= 2^n-1.

%I A371830 #9 Dec 04 2024 10:34:00
%S A371830 1,1,1,1,2,2,1,1,3,6,10,10,6,3,1,1,4,13,39,97,187,290,365,365,290,187,
%T A371830 97,39,13,4,1,1,5,23,111,514,2160,8035,26195,74382,183710,395498,
%U A371830 744592,1229846,1787148,2289929,2591163,2591163,2289929,1787148,1229846,744592,395498,183710,74382,26195,8035,2160,514,111,23,5,1
%N A371830 Irregular triangle read by rows: T(n,k) is the number of unlabeled n-vertex hypergraphs (or set systems) with k hyperedges (none of which is empty), 0 <= k <= 2^n-1.
%H A371830 Pontus von Brömssen, <a href="/A371830/b371830.txt">Table of n, a(n) for n = 0..2046</a>
%H A371830 Peter H. van der Kamp, <a href="https://arxiv.org/abs/2411.18264">Hypergraphs and homogeneous Lotka-Volterra systems with linear Darboux polynomials</a>, arXiv:2411.18264 [nlin.SI], 2024. See p. 4.
%F A371830 T(n,k) = Sum_{j=0..k} (-1)^(k-j)*A052265(n,j).
%e A371830 Triangle begins:
%e A371830   n\k| 0  1  2  3  4   5   6   7   8   9  10 11 12 13 14 15
%e A371830   ---+-----------------------------------------------------
%e A371830   0  | 1
%e A371830   1  | 1  1
%e A371830   2  | 1  2  2  1
%e A371830   3  | 1  3  6 10 10   6   3   1
%e A371830   4  | 1  4 13 39 97 187 290 365 365 290 187 97 39 13  4  1
%o A371830 (SageMath)
%o A371830 def A371830(n,k):
%o A371830     return sum(1 for G in hypergraphs.nauty(k,n,set_min_size=1))
%Y A371830 Cf. A000612 (row sums), A008406, A052265 (empty hyperedge allowed).
%K A371830 nonn,tabf
%O A371830 0,5
%A A371830 _Pontus von Brömssen_, Apr 07 2024