A373417 - cp's OEIS frontend

A373417 Triangle T(n,k) for the number of permutations in symmetric group S_n with (n-k) fixed points and an even number of non-fixed point cycles. Equivalent to the number of cycles of n items with cycle type defined by non-unity partitions of k<=n that contain an even number of parts.

n	a(n)
0	1
1	1
2	0
3	1
4	0
5	0
6	1
7	0
8	0
9	0
10	1
11	0
12	0
13	0
14	3
15	1
16	0
17	0
18	0
19	15
20	20
21	1
22	0
23	0
24	0
25	45
26	120
27	130
28	1
29	0
30	0
31	0
32	105
33	420
34	910
35	924
36	1
37	0
38	0
39	0
40	210
41	1120
42	3640
43	7392
44	7413
45	1
46	0
47	0
48	0
49	378
50	2520
51	10920
52	33264
53	66717
54	66744
55	1
56	0
57	0
58	0
59	630
60	5040
61	27300
62	110880
63	333585
64	667440
65	667476

[1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 1, 0, 0, 0, 15, 20, 1, 0, 0, 0, 45, 120, 130, 1, 0, 0, 0, 105, 420, 910, 924, 1, 0, 0, 0, 210, 1120, 3640, 7392, 7413, 1, 0, 0, 0, 378, 2520, 10920, 33264, 66717, 66744, 1, 0, 0, 0, 630, 5040, 27300, 110880, 333585, 667440, 667476]

cp's OEIS Frontend

A373417 Triangle T(n,k) for the number of permutations in symmetric group S_n with (n-k) fixed points and an even number of non-fixed point cycles. Equivalent to the number of cycles of n items with cycle type defined by non-unity partitions of k<=n that contain an even number of parts.

Table of values

List of values