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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A162979 Triangle read by rows: T(n,k) is the number of alternating (i.e., down-up) permutations of {1,2,...,n} having k fixed points (n >= 0, 0 <= k <= ceiling(n/2)).

Table of values

n a(n)
0 1
1 0
2 1
3 1
4 0
5 1
6 1
7 0
8 2
9 2
10 1
11 6
12 6
13 3
14 1
15 24
16 24
17 11
18 2
19 102
20 102
21 51
22 15
23 2
24 528
25 528
26 252
27 68
28 9
29 2952
30 2952
31 1476
32 458
33 89
34 9
35 19008
36 19008
37 9240
38 2728
39 493
40 44
41 131112
42 131112
43 65556
44 20868
45 4479
46 621
47 44
48 1009728
49 1009728
50 495360
51 152448
52 31182
53 4054
54 265
55 8271792
56 8271792
57 4135896
58 1334928
59 300954
60 47670
61 4959
62 265

List of values

[1, 0, 1, 1, 0, 1, 1, 0, 2, 2, 1, 6, 6, 3, 1, 24, 24, 11, 2, 102, 102, 51, 15, 2, 528, 528, 252, 68, 9, 2952, 2952, 1476, 458, 89, 9, 19008, 19008, 9240, 2728, 493, 44, 131112, 131112, 65556, 20868, 4479, 621, 44, 1009728, 1009728, 495360, 152448, 31182, 4054, 265, 8271792, 8271792, 4135896, 1334928, 300954, 47670, 4959, 265]