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

0,2

Links

Table of n, a(n) for n=0..12.

John Tyler Rascoe, Python program.

Example

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}}.

Prog

(Python) # see linked program

Crossrefs

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

Sequence in context: A055512 A078973 A208650 * A152480 A001660 A368139

Adjacent sequences: A374450 A374451 A374452 * A374454 A374455 A374456

Keyword

nonn,more

Author

John Tyler Rascoe, Jul 08 2024

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

Status

approved