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%I #20 Oct 30 2023 15:33:22
%S 1,1,2,5,16,61,280,1501,9394,68647,591570,6108298,77162708,1219779207,
%T 24648006828,647865966973,22437052221282,1032905858402302,
%U 63591727342096158,5258562027225785955,586001891321599337103,88241281449605821921186,17996565026907866304071630
%N Number of unlabeled ranked posets with n elements.
%C A partially ordered set is ranked if there is a function from the poset elements to the integers such that the function value of a covering element is precisely one larger than the function value of the covered element. This is called graded by some authors.
%H Andrew Howroyd, <a href="/A361920/b361920.txt">Table of n, a(n) for n = 0..40</a>
%e For n=5, A000112(n) - a(n) = 63 - 61 = 2 because we have 2 posets with 5 elements that are not ranked: a<b<c<d a<e<d and a<c<e a<d b<d b<e where < means "is covered by". - _Geoffrey Critzer_, Oct 29 2023
%o (Sage) sum(1 for P in posets(n) if P.is_ranked())
%o (PARI) \\ See PARI link in A361953 for program code.
%o A361920seq(20) \\ _Andrew Howroyd_, Apr 01 2023
%Y Row sums of A361953.
%Y Cf. A000112, A001833 (labeled), A223911, A361912, A361955.
%K nonn
%O 0,3
%A _Martin Rubey_, Mar 29 2023
%E Terms a(8) and beyond from _Andrew Howroyd_, Mar 31 2023
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