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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.

A261319 Number of set partitions C'_t(n) of {1,2,...,t} into at most n parts, with an even number of elements in each part distinguished by marks and such that no part contains both 1 and t (each unmarked) or both i and i+1 (each unmarked) for some i with 1 <= i < t; triangle C'_t(n), t>=0, 0<=n<=t, read by rows.

Table of values

n a(n)
0 1
1 0
2 0
3 0
4 1
5 2
6 0
7 0
8 3
9 4
10 0
11 1
12 11
13 19
14 20
15 0
16 0
17 30
18 80
19 95
20 96
21 0
22 1
23 92
24 372
25 527
26 551
27 552
28 0
29 0
30 273
31 1764
32 3129
33 3500
34 3535
35 3536
36 0
37 1
38 821
39 8549
40 19595
41 24299
42 25055
43 25103
44 25104

List of values

[1, 0, 0, 0, 1, 2, 0, 0, 3, 4, 0, 1, 11, 19, 20, 0, 0, 30, 80, 95, 96, 0, 1, 92, 372, 527, 551, 552, 0, 0, 273, 1764, 3129, 3500, 3535, 3536, 0, 1, 821, 8549, 19595, 24299, 25055, 25103, 25104]

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