A098825 - cp's OEIS frontend

A098825 Triangle read by rows: T(n,k) = number of partial derangements, that is, the number of permutations of n distinct, ordered items in which exactly k of the items are in their natural ordered positions, for n >= 0, k = n, n-1, ..., 1, 0.

n	a(n)
0	1
1	1
2	0
3	1
4	0
5	1
6	1
7	0
8	3
9	2
10	1
11	0
12	6
13	8
14	9
15	1
16	0
17	10
18	20
19	45
20	44
21	1
22	0
23	15
24	40
25	135
26	264
27	265
28	1
29	0
30	21
31	70
32	315
33	924
34	1855
35	1854
36	1
37	0
38	28
39	112
40	630
41	2464
42	7420
43	14832
44	14833
45	1
46	0
47	36
48	168
49	1134
50	5544
51	22260
52	66744
53	133497
54	133496
55	1
56	0
57	45
58	240
59	1890
60	11088
61	55650
62	222480
63	667485
64	1334960
65	1334961

[1, 1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 6, 8, 9, 1, 0, 10, 20, 45, 44, 1, 0, 15, 40, 135, 264, 265, 1, 0, 21, 70, 315, 924, 1855, 1854, 1, 0, 28, 112, 630, 2464, 7420, 14832, 14833, 1, 0, 36, 168, 1134, 5544, 22260, 66744, 133497, 133496, 1, 0, 45, 240, 1890, 11088, 55650, 222480, 667485, 1334960, 1334961]

cp's OEIS Frontend

A098825 Triangle read by rows: T(n,k) = number of partial derangements, that is, the number of permutations of n distinct, ordered items in which exactly k of the items are in their natural ordered positions, for n >= 0, k = n, n-1, ..., 1, 0.

Table of values

List of values