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 A379706 #13 Jan 06 2025 06:13:25
%S A379706 0,0,1,10,97,1418,40005,2350474,286192257,71213783154,35883905262757,
%T A379706 36419649682704418,74221659280476132145,303193505953871645554778,
%U A379706 2480118046704094643352342117,40601989176407026666590990389338,1329877330167226219547875498464450945,87134888326188320631048795061602782878050
%N A379706 Number of nonempty labeled antichains of subsets of [n] such that the largest subset is of size 2.
%F A379706 a(n) = Sum_{i=0..n-2} binomial(n,i) * (2^binomial(n-i,2) - 1).
%e A379706 a(2) = 1: {{1,2}}.
%e A379706 a(3) = 10: {{1,2}}, {{1,3}}, {{2,3}}, {{1,2},{3}}, {{1,3},{2}}, {{2,3},{1}}, {{1,2},{1,3}}, {{1,2},{2,3}}, {{1,3},{2,3}}, {{1,2},{1,3},{2,3}}.
%o A379706 (Python)
%o A379706 from math import comb
%o A379706 def A379706(n): return sum(comb(n,i)*(2**comb(n-i,2) - 1) for i in range(n-1))
%Y A379706 Cf. A000225, A000372, A036239, A126883, A379707, (column k=2 of A379712).
%K A379706 nonn,easy
%O A379706 0,4
%A A379706 _John Tyler Rascoe_, Dec 30 2024