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