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 A374453 #36 Jul 17 2024 10:40:47
%S A374453 1,2,6,36,547,26672,5120069,4581266029,21912279450653,
%T A374453 627026135401140277,118043015040470215561725,
%U A374453 158758107128989643461422723149,1641097327889006717487651007699748392
%N A374453 Number of set-systems S composed of nonempty subsets of [n] such that any element k in S appears at most k times.
%H A374453 John Tyler Rascoe, <a href="/A374453/a374453_2.py.txt">Python program</a>.
%e A374453 In the set-system: {{2, 3, 5},{3, 4, 5},{1, 3},{2}} no element k appears more than k times, so it is counted under a(5) = 26672.
%e A374453 a(n) for n = 0..2 counts the following set-systems:
%e A374453 a(0) = 1: {}.
%e A374453 a(1) = 2: {}, {{1}}.
%e A374453 a(2) = 6: {}, {{1}}, {{2}}, {{1},{2}}, {{1,2}}, {{1,2},{2}}.
%o A374453 (Python) # see linked program
%Y A374453 Cf. A036239, A072444, A072445, A306021, A323818.
%K A374453 nonn,more
%O A374453 0,2
%A A374453 _John Tyler Rascoe_, Jul 08 2024
%E A374453 a(7)-a(8) from _Alois P. Heinz_, Jul 09 2024
%E A374453 a(9) from _Alois P. Heinz_, Jul 15 2024
%E A374453 a(10)-a(12) from _Christian Sievers_, Jul 17 2024