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%I #13 Jul 27 2022 11:53:23
%S 1,0,0,1,4,28,234,2585,36326,646405,14528011,412212506
%N Number of unlabeled prime posets with n elements.
%C A poset P is called prime if it is not decomposable. A poset Q is called decomposable if Q can be obtained as the composition (lexicographic product) of the outer poset Q' and the inner posets Qi, 1 <= i <= r, where |Q'| = r > 1 and at least one of the posets Qi is nonsingleton.
%H S. M. Khamis, <a href="https://www.researchgate.net/publication/268251436_On_numerical_counting_of_prime_UPO_and_the_general_type_of_posets_according_to_heights">On numerical counting of prime, UPO, and the general type of posets according to heights</a>, Congressus Numerantium, 146 (2000), 157-171.
%H S. M. Khamis, <a href="http://research.asu.edu.eg/handle/123456789/1132">Recognition of prime posets and one of its applications</a>, J. Egypt. Math. Soc., 14 (1) (2006), 5-13.
%Y Cf. A000112, A003430, A202182.
%K nonn,more
%O 1,5
%A _Salah Uddin Mohammad_, Jun 03 2022