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A361958 Triangle read by rows: T(n,k) is the number of connected unlabeled tiered posets with n elements and height k.

%I A361958 #10 Apr 03 2023 21:47:55
%S A361958 1,0,1,0,2,1,0,4,3,1,0,10,10,4,1,0,27,34,16,5,1,0,88,146,66,23,6,1,0,
%T A361958 328,739,326,106,31,7,1,0,1460,4671,1932,566,156,40,8,1,0,7799,37088,
%U A361958 14104,3577,878,217,50,9,1,0,51196,376524,128652,27563,5740,1276,290,61,10,1
%N A361958 Triangle read by rows: T(n,k) is the number of connected unlabeled tiered posets with n elements and height k.
%C A361958 A tiered poset is a partially ordered set in which every maximal chain has the same length.
%H A361958 Andrew Howroyd, <a href="/A361958/b361958.txt">Table of n, a(n) for n = 1..820</a> (rows 1..40).
%F A361958 Column k is the inverse Euler transform of column k of A361957.
%e A361958 Triangle begins:
%e A361958   1;
%e A361958   0,    1;
%e A361958   0,    2,    1;
%e A361958   0,    4,    3,    1;
%e A361958   0,   10,   10,    4,   1;
%e A361958   0,   27,   34,   16,   5,   1;
%e A361958   0,   88,  146,   66,  23,   6,  1;
%e A361958   0,  328,  739,  326, 106,  31,  7, 1;
%e A361958   0, 1460, 4671, 1932, 566, 156, 40, 8, 1;
%e A361958   ...
%o A361958 (PARI) \\ See PARI link in A361957 for program code.
%o A361958 { my(A=A361958tabl(9)); for(i=1, #A, print(A[i, 1..i])) }
%Y A361958 Row sums are A361959.
%Y A361958 Cf. A361954, A361957 (not necessarily connected).
%K A361958 nonn,tabl
%O A361958 1,5
%A A361958 _Andrew Howroyd_, Apr 03 2023