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Number of unlabeled connected weakly graded (ranked) posets with n elements.
3

%I #8 Apr 01 2023 15:48:53

%S 1,1,1,3,10,42,202,1146,7493,56996,508609,5414635,70214227,1134439731,

%T 23331152887,621768153861,21761221300058,1009759125475973,

%U 62534859409597022,5193886959561972984,580677490292990902682,87649885799470898359728,17907726747155924589913398

%N Number of unlabeled connected weakly graded (ranked) posets with n elements.

%C Here weakly graded means that there exists a rank function rk from the poset to the integers such that whenever v covers w in the poset, we have rk(v) = rk(w) + 1.

%H Andrew Howroyd, <a href="/A361955/b361955.txt">Table of n, a(n) for n = 0..40</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Graded_poset">Graded poset</a>.

%F Inverse Euler transform of A361920.

%o (PARI) \\ See PARI link in A361953 for program code.

%o A361955seq(20)

%Y Row sums of A361954.

%Y Cf. A000608, A361920, A361953.

%K nonn

%O 0,4

%A _Andrew Howroyd_, Mar 31 2023