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A361952
Array read by antidiagonals: T(n,k) is the number of unlabeled posets with n elements together with a function rk mapping each element to a rank between 1 and k such that whenever v covers w in the poset then rk(v) = rk(w) + 1.
3
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 4, 1, 0, 1, 4, 8, 8, 1, 0, 1, 5, 13, 21, 17, 1, 0, 1, 6, 19, 40, 58, 38, 1, 0, 1, 7, 26, 66, 126, 172, 94, 1, 0, 1, 8, 34, 100, 228, 420, 569, 258, 1, 0, 1, 9, 43, 143, 373, 816, 1537, 2148, 815, 1, 0, 1, 10, 53, 196, 571, 1412, 3140, 6342, 9538, 3038, 1, 0
OFFSET
0,8
COMMENTS
A poset is counted once for each admissible ranking function. This is an intermediate step in the computation of A361953 where each graded poset is counted exactly once.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..860 (first 41 antidiagonals).
EXAMPLE
Array begins:
============================================
n/k| 0 1 2 3 4 5 6 7 ...
---+----------------------------------------
0 | 1 1 1 1 1 1 1 1 ...
1 | 0 1 2 3 4 5 6 7 ...
2 | 0 1 4 8 13 19 26 34 ...
3 | 0 1 8 21 40 66 100 143 ...
4 | 0 1 17 58 126 228 373 571 ...
5 | 0 1 38 172 420 816 1412 2272 ...
6 | 0 1 94 569 1537 3140 5631 9351 ...
7 | 0 1 258 2148 6342 13383 24410 41097 ...
...
PROG
(PARI) \\ See Links in A361953 for program.
{ my(A=A361952tabl(7)); for(i=1, #A, print(A[i, ])) }
CROSSREFS
Columns k=0..2 are A000007, A000012, A049312.
Rows n=0..4 are A000012, A000027, A034856, A137742.
The labeled version is A361950.
Cf. A361953.
Sequence in context: A350364 A358575 A259475 * A323224 A118340 A213276
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 31 2023
STATUS
approved