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Triangle read by rows: T(n,k) is the number of connected unlabeled tiered posets with n elements and height k.
3

%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