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A098071 Triangle read by rows: T(n,k) is number of peakless Motzkin paths of length n and having k uhh...hd's starting at level 0, where u=(1,1), h=(1,0) and d=(1,-1) (can be easily expressed using RNA secondary structure terminology).

Table of values

n a(n)
0 1
1 1
2 1
3 1
4 1
5 1
6 3
7 2
8 6
9 6
10 10
11 1
12 17
13 15
14 5
15 44
16 23
17 15
18 107
19 42
20 35
21 1
22 252
23 94
24 70
25 7
26 588
27 233
28 129
29 28
30 1376
31 585
32 237
33 84
34 1
35 3245
36 1441
37 468
38 210
39 9
40 7717
41 3481
42 1026
43 466
44 45
45 18485
46 8319
47 2434
48 968
49 165
50 1
51 44535
52 19835
53 5972
54 1984
55 495
56 11
57 107796
58 47436

List of values

[1, 1, 1, 1, 1, 1, 3, 2, 6, 6, 10, 1, 17, 15, 5, 44, 23, 15, 107, 42, 35, 1, 252, 94, 70, 7, 588, 233, 129, 28, 1376, 585, 237, 84, 1, 3245, 1441, 468, 210, 9, 7717, 3481, 1026, 466, 45, 18485, 8319, 2434, 968, 165, 1, 44535, 19835, 5972, 1984, 495, 11, 107796, 47436]