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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.

A144088 T(n,k) is the number of partial bijections (or subpermutations) of an n-element set with exactly k fixed points.

Table of values

n a(n)
0 1
1 1
2 1
3 4
4 2
5 1
6 18
7 12
8 3
9 1
10 108
11 72
12 24
13 4
14 1
15 780
16 540
17 180
18 40
19 5
20 1
21 6600
22 4680
23 1620
24 360
25 60
26 6
27 1
28 63840
29 46200
30 16380
31 3780
32 630
33 84
34 7
35 1
36 693840
37 510720
38 184800
39 43680
40 7560
41 1008
42 112
43 8
44 1
45 8361360
46 6244560
47 2298240
48 554400
49 98280
50 13608
51 1512
52 144
53 9
54 1

List of values

[1, 1, 1, 4, 2, 1, 18, 12, 3, 1, 108, 72, 24, 4, 1, 780, 540, 180, 40, 5, 1, 6600, 4680, 1620, 360, 60, 6, 1, 63840, 46200, 16380, 3780, 630, 84, 7, 1, 693840, 510720, 184800, 43680, 7560, 1008, 112, 8, 1, 8361360, 6244560, 2298240, 554400, 98280, 13608, 1512, 144, 9, 1]