This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A147821 #37 Apr 12 2020 03:11:49
%S A147821 108,6180,83952,601944,2991576,11662056,38167920,109368864,282174948,
%T A147821 668565612,1475938464,3069513720,6065522736,11466274512,20850952608,
%U A147821 36639176832,62447999580,103567126068,167581781136,265177823064,411169457160,625796259000
%N A147821 Number of consistent sets of 5 irreflexive binary order relationships over n objects.
%C A147821 It seems that a(n) = A081064(n,5) is the number of labeled acyclic directed graphs with n nodes and k = 5 arcs (see Rodionov (1992)). The reason is that we may label the graphs with the n objects and draw an arc from X towards Y if and only if X < Y. The 5 arcs of the directed graph correspond to the 3-set of binary order relationships and they are consistent because the directed graph is acyclic. - _Petros Hadjicostas_, Apr 10 2020
%H A147821 V. I. Rodionov, <a href="https://doi.org/10.1016/0012-365X(92)90155-9">On the number of labeled acyclic digraphs</a>, Discr. Math. 105 (1-3) (1992), 319-321.
%F A147821 a(n) = (n-3)*(n-2)*(n-1)*n*(n^6 + n^5 - 15*n^4 - 45*n^3 - 4*n^2 + 326*n + 900)/120. - _Vaclav Kotesovec_, Apr 11 2020
%F A147821 Conjectures from _Colin Barker_, Apr 11 2020: (Start)
%F A147821 G.f.: 12*x^4*(9 + 416*x + 1826*x^2 + 46*x^3 + 291*x^4 - 78*x^5 + 10*x^6) / (1 - x)^11.
%F A147821 a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>12.
%F A147821 (End)
%p A147821 a := n -> (1/120)*(n-3)*(n-2)*(n-1)*n*(n*(n*(n*(n*(n^2+n-15)-45)-4)+326)+900):
%p A147821 seq(a(n), n=4..25); # _Peter Luschny_, Apr 11 2020
%t A147821 Table[(n - 3)*(n - 2)*(n - 1)*n*(n^6 + n^5 - 15*n^4 - 45*n^3 - 4*n^2 + 326*n + 900)/120, {n, 4, 25}] (* _Wesley Ivan Hurt_, Apr 11 2020 *)
%Y A147821 Related sequences for the number of consistent sets of k irreflexive binary order relationships over n objects: A147796 (k = 3), A147817 (k = 4), A147860 (k = 6), A147872 (k = 7), A147881 (k = 8), A147883 (k = 9), A147964 (k = 10).
%Y A147821 Column k = 5 of A081064.
%K A147821 nonn,easy
%O A147821 4,1
%A A147821 _R. H. Hardin_, May 04 2009
%E A147821 More terms from _Vaclav Kotesovec_, Apr 11 2020
%E A147821 Offset changed by _Petros Hadjicostas_, Apr 11 2020