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A361954 Triangle read by rows: T(n,k) is the number of unlabeled connected weakly graded (ranked) posets with n elements and rank k.

%I A361954 #10 Apr 03 2023 21:09:29
%S A361954 1,0,1,0,2,1,0,4,5,1,0,10,23,8,1,0,27,107,56,11,1,0,88,557,388,98,14,
%T A361954 1,0,328,3271,2888,839,149,17,1,0,1460,22424,23900,7512,1470,209,20,1,
%U A361954 0,7799,183273,226807,73405,14715,2308,278,23,1
%N A361954 Triangle read by rows: T(n,k) is the number of unlabeled connected weakly graded (ranked) posets with n elements and rank k.
%C A361954 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 A361954 Andrew Howroyd, <a href="/A361954/b361954.txt">Table of n, a(n) for n = 1..820</a> (rows 1..40)
%H A361954 Wikipedia, <a href="https://en.wikipedia.org/wiki/Graded_poset">Graded poset</a>.
%e A361954 Triangle begins:
%e A361954   1;
%e A361954   0,   1;
%e A361954   0,   2,    1;
%e A361954   0,   4,    5,    1;
%e A361954   0,  10,   23,    8,   1;
%e A361954   0,  27,  107,   56,  11,   1;
%e A361954   0,  88,  557,  388,  98,  14,  1;
%e A361954   0, 328, 3271, 2888, 839, 149, 17, 1;
%e A361954   ...
%o A361954 (PARI) \\ See PARI link in A361953 for program code.
%o A361954 { my(A=A361954tabl(8)); for(i=1, #A, print(A[i, 1..i])) }
%Y A361954 Column k=2 is A007776.
%Y A361954 Row sums are A361955.
%Y A361954 Cf. A342500, A361953 (not necessarily connected).
%K A361954 nonn,tabl
%O A361954 1,5
%A A361954 _Andrew Howroyd_, Mar 31 2023