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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.

A261318 Number of set partitions T'_t(n) of {1,2,...,t} into exactly n parts, with an even number of elements in each part distinguished by marks, and such that no part contains both 1 and t with 1 unmarked or both i and i+1 with i+1 unmarked for some i with 1 <= i < t; triangle T'_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 1
6 0
7 0
8 3
9 1
10 0
11 1
12 10
13 8
14 1
15 0
16 0
17 30
18 50
19 15
20 1
21 0
22 1
23 91
24 280
25 155
26 24
27 1
28 0
29 0
30 273
31 1491
32 1365
33 371
34 35
35 1
36 0
37 1
38 820
39 7728
40 11046
41 4704
42 756
43 48
44 1
45 0
46 0
47 2460
48 39460
49 85050
50 53382
51 13020
52 1380
53 63
54 1

List of values

[1, 0, 0, 0, 1, 1, 0, 0, 3, 1, 0, 1, 10, 8, 1, 0, 0, 30, 50, 15, 1, 0, 1, 91, 280, 155, 24, 1, 0, 0, 273, 1491, 1365, 371, 35, 1, 0, 1, 820, 7728, 11046, 4704, 756, 48, 1, 0, 0, 2460, 39460, 85050, 53382, 13020, 1380, 63, 1]

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