%I #13 Apr 03 2023 21:09:24

%S 1,0,1,0,1,1,0,1,2,1,0,1,5,3,1,0,1,12,10,4,1,0,1,35,35,16,5,1,0,1,108,

%T 149,66,23,6,1,0,1,393,755,327,106,31,7,1,0,1,1666,4736,1936,566,156,

%U 40,8,1,0,1,8543,37394,14130,3578,878,217,50,9,1

%N Triangle read by rows: T(n,k) is the number of 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="/A361957/b361957.txt">Table of n, a(n) for n = 0..860</a> (rows 0..40).

%H Andrew Howroyd, <a href="/A361957/a361957.gp.txt">PARI Program</a>, Apr 2023.

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 1, 1;

%e 0, 1, 2, 1;

%e 0, 1, 5, 3, 1;

%e 0, 1, 12, 10, 4, 1;

%e 0, 1, 35, 35, 16, 5, 1;

%e 0, 1, 108, 149, 66, 23, 6, 1;

%e 0, 1, 393, 755, 327, 106, 31, 7, 1;

%e 0, 1, 1666, 4736, 1936, 566, 156, 40, 8, 1;

%e ...

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

%o { my(A=A361957tabl(9)); for(i=1, #A, print(A[i, 1..i])) }

%Y Row sums are A361912.

%Y Column k=2 is A055192.

%Y The labeled version is A361956.

%Y Cf. A361953, A361958 (connected).

%K nonn,tabl

%O 0,9

%A _Andrew Howroyd_, Apr 03 2023