A186363 - cp's OEIS frontend

A186363 Triangle read by rows: T(n,k) is the number of cycle-up-down permutations of {1,2,...,n} having k fixed points (0 <= k <= n). A permutation is said to be cycle-up-down if it is a product of up-down cycles. A cycle (b(1), b(2), ...) is said to be up-down if, when written with its smallest element in the first position, it satisfies b(1) < b(2) > b(3) < ... .

n	a(n)
0	1
1	0
2	1
3	1
4	0
5	1
6	1
7	3
8	0
9	1
10	5
11	4
12	6
13	0
14	1
15	15
16	25
17	10
18	10
19	0
20	1
21	71
22	90
23	75
24	20
25	15
26	0
27	1
28	341
29	497
30	315
31	175
32	35
33	21
34	0
35	1
36	1945
37	2728
38	1988
39	840
40	350
41	56
42	28
43	0
44	1
45	12135
46	17505
47	12276
48	5964
49	1890
50	630
51	84
52	36
53	0
54	1
55	84091
56	121350
57	87525
58	40920
59	14910
60	3780
61	1050
62	120
63	45
64	0
65	1

[1, 0, 1, 1, 0, 1, 1, 3, 0, 1, 5, 4, 6, 0, 1, 15, 25, 10, 10, 0, 1, 71, 90, 75, 20, 15, 0, 1, 341, 497, 315, 175, 35, 21, 0, 1, 1945, 2728, 1988, 840, 350, 56, 28, 0, 1, 12135, 17505, 12276, 5964, 1890, 630, 84, 36, 0, 1, 84091, 121350, 87525, 40920, 14910, 3780, 1050, 120, 45, 0, 1]

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