A114709 - cp's OEIS frontend

A114709 Triangle read by rows: T(n,k) is the number of hill-free Schroeder paths of length 2n that have k horizontal steps on the x-axis (0<=k<=n). 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.

n	a(n)
0	1
1	0
2	1
3	2
4	0
5	1
6	6
7	4
8	0
9	1
10	26
11	12
12	6
13	0
14	1
15	114
16	56
17	18
18	8
19	0
20	1
21	526
22	252
23	90
24	24
25	10
26	0
27	1
28	2502
29	1192
30	414
31	128
32	30
33	12
34	0
35	1
36	12194
37	5772
38	2006
39	600
40	170
41	36
42	14
43	0
44	1
45	60570
46	28536
47	9882
48	2976
49	810
50	216
51	42
52	16
53	0
54	1
55	305526
56	143388
57	49554
58	14904
59	4110
60	1044

[1, 0, 1, 2, 0, 1, 6, 4, 0, 1, 26, 12, 6, 0, 1, 114, 56, 18, 8, 0, 1, 526, 252, 90, 24, 10, 0, 1, 2502, 1192, 414, 128, 30, 12, 0, 1, 12194, 5772, 2006, 600, 170, 36, 14, 0, 1, 60570, 28536, 9882, 2976, 810, 216, 42, 16, 0, 1, 305526, 143388, 49554, 14904, 4110, 1044]

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