A114706 - cp's OEIS frontend

A114706 Triangle read by rows: T(n,k) is the number of hill-free Schroeder paths of length 2n and having k ascents (n>=1; 0<=k<=n-1). A Schroeder path of length 2n is a lattice path from (0,0) to (2n,0) consisting of U=(1,1), D=(1,-1) and H=(2,0) steps and never going below the x-axis. A hill is a peak at height 1. An ascent in a Schroeder path is a maximal sequence of consecutive U steps.

n	a(n)
1	1
2	1
3	2
4	1
5	8
6	2
7	1
8	22
9	20
10	2
11	1
12	52
13	106
14	36
15	2
16	1
17	114
18	420
19	310
20	56
21	2
22	1
23	240
24	1410
25	1840
26	706
27	80
28	2
29	1
30	494
31	4260
32	8714
33	5832
34	1382
35	108
36	2
37	1
38	1004
39	11978
40	35484
41	36898
42	15100
43	2442
44	140
45	2
46	1
47	2026
48	31988
49	129758
50	194216
51	122674
52	34012
53	4006
54	176
55	2
56	1

[1, 1, 2, 1, 8, 2, 1, 22, 20, 2, 1, 52, 106, 36, 2, 1, 114, 420, 310, 56, 2, 1, 240, 1410, 1840, 706, 80, 2, 1, 494, 4260, 8714, 5832, 1382, 108, 2, 1, 1004, 11978, 35484, 36898, 15100, 2442, 140, 2, 1, 2026, 31988, 129758, 194216, 122674, 34012, 4006, 176, 2, 1]

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