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A177250 Triangle read by rows: T(n,k) is the number of permutations of [n] having k adjacent 3-cycles (0 <= k <= floor(n/3)), i.e., having k cycles of the form (i, i+1, i+2).

Table of values

n a(n)
0 1
1 1
2 2
3 5
4 1
5 22
6 2
7 114
8 6
9 697
10 22
11 1
12 4923
13 114
14 3
15 39612
16 696
17 12
18 357899
19 4923
20 57
21 1
22 3588836
23 39612
24 348
25 4
26 39556420
27 357900
28 2460
29 20
30 475392841
31 3588836
32 19806
33 116
34 1
35 6187284605
36 39556420
37 178950
38 820
39 5
40 86701097310
41 475392840
42 1794420
43 6600
44 30

List of values

[1, 1, 2, 5, 1, 22, 2, 114, 6, 697, 22, 1, 4923, 114, 3, 39612, 696, 12, 357899, 4923, 57, 1, 3588836, 39612, 348, 4, 39556420, 357900, 2460, 20, 475392841, 3588836, 19806, 116, 1, 6187284605, 39556420, 178950, 820, 5, 86701097310, 475392840, 1794420, 6600, 30]