A374453 Number of set-systems S composed of nonempty subsets of [n] such that any element k in S appears at most k times.
1, 2, 6, 36, 547, 26672, 5120069, 4581266029, 21912279450653, 627026135401140277, 118043015040470215561725, 158758107128989643461422723149, 1641097327889006717487651007699748392
Offset: 0
Examples
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.
a(n) for n = 0..2 counts the following set-systems:
a(0) = 1: {}.
a(1) = 2: {}, {{1}}.
a(2) = 6: {}, {{1}}, {{2}}, {{1},{2}}, {{1,2}}, {{1,2},{2}}.
Links
- John Tyler Rascoe, Python program.
Programs
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Python
# see linked program
Extensions
a(7)-a(8) from Alois P. Heinz, Jul 09 2024
a(9) from Alois P. Heinz, Jul 15 2024
a(10)-a(12) from Christian Sievers, Jul 17 2024