A114692 - cp's OEIS frontend

A114692 Triangle read by rows: T(n,k) is the number of hill-free Schroeder paths of length 2n that have k returns to the x-axis (0<=k<=floor(n/2)). 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	1
2	1
3	2
4	1
5	10
6	1
7	40
8	4
9	1
10	160
11	36
12	1
13	674
14	220
15	8
16	1
17	2994
18	1180
19	104
20	1
21	13872
22	6056
23	848
24	16
25	1
26	66336
27	30760
28	5680
29	272
30	1
31	324898
32	156632
33	34528
34	2768
35	32
36	1
37	1621178
38	803096
39	199552
40	22224
41	672
42	1
43	8210904
44	4150444
45	1122736
46	156528
47	8192
48	64
49	1

[1, 1, 1, 2, 1, 10, 1, 40, 4, 1, 160, 36, 1, 674, 220, 8, 1, 2994, 1180, 104, 1, 13872, 6056, 848, 16, 1, 66336, 30760, 5680, 272, 1, 324898, 156632, 34528, 2768, 32, 1, 1621178, 803096, 199552, 22224, 672, 1, 8210904, 4150444, 1122736, 156528, 8192, 64, 1]

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