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A322383 Number T(n,k) of entries in the k-th cycles of all permutations of [n] when cycles are ordered by increasing lengths (and increasing smallest elements); triangle T(n,k), n>=1, 1<=k<=n, read by rows.

Table of values

n a(n)
1 1
2 3
3 1
4 10
5 7
6 1
7 45
8 37
9 13
10 1
11 236
12 241
13 101
14 21
15 1
16 1505
17 1661
18 896
19 226
20 31
21 1
22 10914
23 13301
24 7967
25 2612
26 442
27 43
28 1
29 90601
30 117209
31 78205
32 29261
33 6441
34 785
35 57
36 1
37 837304
38 1150297
39 827521
40 346453
41 88909
42 14065
43 1297
44 73
45 1
46 8610129
47 12314329
48 9507454
49 4338214
50 1253104
51 234646
52 28006
53 2026
54 91
55 1

List of values

[1, 3, 1, 10, 7, 1, 45, 37, 13, 1, 236, 241, 101, 21, 1, 1505, 1661, 896, 226, 31, 1, 10914, 13301, 7967, 2612, 442, 43, 1, 90601, 117209, 78205, 29261, 6441, 785, 57, 1, 837304, 1150297, 827521, 346453, 88909, 14065, 1297, 73, 1, 8610129, 12314329, 9507454, 4338214, 1253104, 234646, 28006, 2026, 91, 1]