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The number of unlabeled graded posets with n elements.
5

%I #21 Apr 03 2023 21:09:18

%S 1,1,2,4,10,28,93,354,1621,9110,64801,595976,7204091,115561423,

%T 2473540433,70853213144,2720354016419,140170631441858,

%U 9702605436760235,903309202327818566,113234129823368903523,19137461395401601912043,4366007821745938984134203

%N The number of unlabeled graded posets with n elements.

%C A partially ordered set is graded if all maximal chains have the same length. This is called tiered by some authors.

%H Andrew Howroyd, <a href="/A361912/b361912.txt">Table of n, a(n) for n = 0..40</a>

%o (Sage) sum(1 for P in posets(n) if P.is_graded())

%o (PARI) \\ See PARI link in A361957 for program code.

%o A361912seq(20) \\ _Andrew Howroyd_, Apr 03 2023

%Y Row sums of A361957.

%Y Cf. A000112, A223911 (labeled), A001833, A361920, A361959 (connected).

%K nonn

%O 0,3

%A _Martin Rubey_, Mar 29 2023

%E Terms a(8) and beyond from _Andrew Howroyd_, Mar 30 2023