cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

This page as a plain text file.
%I A361952 #10 Apr 01 2023 14:27:39
%S A361952 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,
%T A361952 58,38,1,0,1,7,26,66,126,172,94,1,0,1,8,34,100,228,420,569,258,1,0,1,
%U A361952 9,43,143,373,816,1537,2148,815,1,0,1,10,53,196,571,1412,3140,6342,9538,3038,1,0
%N 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.
%C A361952 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.
%H A361952 Andrew Howroyd, <a href="/A361952/b361952.txt">Table of n, a(n) for n = 0..860</a> (first 41 antidiagonals).
%e A361952 Array begins:
%e A361952 ============================================
%e A361952 n/k| 0 1   2    3    4     5     6     7 ...
%e A361952 ---+----------------------------------------
%e A361952 0  | 1 1   1    1    1     1     1     1 ...
%e A361952 1  | 0 1   2    3    4     5     6     7 ...
%e A361952 2  | 0 1   4    8   13    19    26    34 ...
%e A361952 3  | 0 1   8   21   40    66   100   143 ...
%e A361952 4  | 0 1  17   58  126   228   373   571 ...
%e A361952 5  | 0 1  38  172  420   816  1412  2272 ...
%e A361952 6  | 0 1  94  569 1537  3140  5631  9351 ...
%e A361952 7  | 0 1 258 2148 6342 13383 24410 41097 ...
%e A361952   ...
%o A361952 (PARI) \\ See Links in A361953 for program.
%o A361952 { my(A=A361952tabl(7)); for(i=1, #A, print(A[i,])) }
%Y A361952 Columns k=0..2 are A000007, A000012, A049312.
%Y A361952 Rows n=0..4 are A000012, A000027, A034856, A137742.
%Y A361952 The labeled version is A361950.
%Y A361952 Cf. A361953.
%K A361952 nonn,tabl
%O A361952 0,8
%A A361952 _Andrew Howroyd_, Mar 31 2023