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Number of set-systems S composed of nonempty subsets of [n] such that any element k in S appears at most k times.
1

%I #36 Jul 17 2024 10:40:47

%S 1,2,6,36,547,26672,5120069,4581266029,21912279450653,

%T 627026135401140277,118043015040470215561725,

%U 158758107128989643461422723149,1641097327889006717487651007699748392

%N Number of set-systems S composed of nonempty subsets of [n] such that any element k in S appears at most k times.

%H John Tyler Rascoe, <a href="/A374453/a374453_2.py.txt">Python program</a>.

%e 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 a(n) for n = 0..2 counts the following set-systems:

%e a(0) = 1: {}.

%e a(1) = 2: {}, {{1}}.

%e a(2) = 6: {}, {{1}}, {{2}}, {{1},{2}}, {{1,2}}, {{1,2},{2}}.

%o (Python) # see linked program

%Y Cf. A036239, A072444, A072445, A306021, A323818.

%K nonn,more

%O 0,2

%A _John Tyler Rascoe_, Jul 08 2024

%E a(7)-a(8) from _Alois P. Heinz_, Jul 09 2024

%E a(9) from _Alois P. Heinz_, Jul 15 2024

%E a(10)-a(12) from _Christian Sievers_, Jul 17 2024