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A125183 Triangle read by rows: T(n,k) is the number of permutations p of {1,2,...,n} such that the set {|p(i)-i|, i=1,2,...,n} has exactly k elements (1<=k<=n).

Table of values

n a(n)
1 1
2 2
3 0
4 1
5 5
6 0
7 3
8 11
9 6
10 4
11 1
12 28
13 55
14 32
15 4
16 3
17 69
18 210
19 330
20 108
21 0
22 1
23 102
24 846
25 2177
26 1590
27 324
28 0
29 4
30 279
31 2694
32 11221
33 17578
34 7624
35 888
36 32
37 1
38 328
39 7791
40 54777
41 135993
42 123474
43 37524
44 2896
45 96
46 3
47 961
48 24032
49 227906
50 914364
51 1427342
52 839904
53 182824
54 11464
55 0

List of values

[1, 2, 0, 1, 5, 0, 3, 11, 6, 4, 1, 28, 55, 32, 4, 3, 69, 210, 330, 108, 0, 1, 102, 846, 2177, 1590, 324, 0, 4, 279, 2694, 11221, 17578, 7624, 888, 32, 1, 328, 7791, 54777, 135993, 123474, 37524, 2896, 96, 3, 961, 24032, 227906, 914364, 1427342, 839904, 182824, 11464, 0]