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 A384105 #12 May 21 2025 15:50:17
%S A384105 1,1,1,3,4,3,16,36,36,16,218,752,1104,752,218,9608,45960,90416,90416,
%T A384105 45960,9608,1540944,9133760,22692704,30194176,22692704,9133760,
%U A384105 1540944,882033440,6154473664,18425858880,30679088480,30679088480,18425858880,6154473664,882033440
%N A384105 Triangle read by rows: T(n,k) is the number of binary relations on a set of n objects, exactly k of which are self referencing, 0 <= k <= n.
%C A384105 Also the number of essentially different simple digraphs on a node set A of size n with a distinguished subset B of size k, where elements are indistinguishable within B and within A \ B.
%H A384105 Peter Dolland, <a href="/A384105/a384105_1.py.txt">Python calculation of T(n,k)</a>
%F A384105 T(n,k) = T(n,n-k).
%F A384105 T(n,0) = T(n,n) = A000273(n).
%F A384105 T(n,1) = T(n,n-1) = A353996(n+1) = A329874(n,4).
%F A384105 Sum_{k=0..n} T(n,k) = A000595(n).
%e A384105 Triangle starts:
%e A384105 1
%e A384105 1, 1
%e A384105 3, 4, 3
%e A384105 16, 36, 36, 16
%e A384105 218, 752, 1104, 752, 218
%e A384105 9608, 45960, 90416, 90416, 45960, ...
%e A384105 1540944, 9133760, 22692704, 30194176, 22692704, ...
%e A384105 882033440, 6154473664, 18425858880, 30679088480, 30679088480, ...
%e A384105 1793359192848, 14334221970688, 50138592081152, 100240050239744, 125284653092864, ...
%e A384105 ...
%Y A384105 Cf. A000273 (edge cases), A000595 (row sums), A353996, A328874, A383617.
%K A384105 nonn,tabl
%O A384105 0,4
%A A384105 _Peter Dolland_, May 19 2025