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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.

A271023 Number T(n,k) of set partitions of [n] having exactly k pairs (i,j) with i such that i and j are in the same block; triangle T(n,k), n>=0, 0<=k<=n*(n-1)/2 read by rows.

Table of values

n a(n)
0 1
1 1
2 1
3 1
4 1
5 3
6 0
7 1
8 1
9 6
10 3
11 4
12 0
13 0
14 1
15 1
16 10
17 15
18 10
19 10
20 0
21 5
22 0
23 0
24 0
25 1
26 1
27 15
28 45
29 35
30 60
31 0
32 25
33 15
34 0
35 0
36 6
37 0
38 0
39 0
40 0
41 1
42 1
43 21
44 105
45 140
46 210
47 105
48 105
49 105
50 0
51 35
52 21
53 21
54 0
55 0
56 0
57 7
58 0
59 0
60 0
61 0
62 0
63 1
64 1
65 28
66 210
67 476
68 665
69 840
70 350
71 700
72 210

List of values

[1, 1, 1, 1, 1, 3, 0, 1, 1, 6, 3, 4, 0, 0, 1, 1, 10, 15, 10, 10, 0, 5, 0, 0, 0, 1, 1, 15, 45, 35, 60, 0, 25, 15, 0, 0, 6, 0, 0, 0, 0, 1, 1, 21, 105, 140, 210, 105, 105, 105, 0, 35, 21, 21, 0, 0, 0, 7, 0, 0, 0, 0, 0, 1, 1, 28, 210, 476, 665, 840, 350, 700, 210]

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