A114655 - cp's OEIS frontend

A114655 Triangle read by rows: T(n,k) is the number of Schroeder paths of length 2n and having k weak ascents (1<=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 weak ascent in a Schroeder path is a maximal sequence of consecutive U and H steps.

n	a(n)
1	2
2	4
3	2
4	8
5	12
6	2
7	16
8	48
9	24
10	2
11	32
12	160
13	160
14	40
15	2
16	64
17	480
18	800
19	400
20	60
21	2
22	128
23	1344
24	3360
25	2800
26	840
27	84
28	2
29	256
30	3584
31	12544
32	15680
33	7840
34	1568
35	112
36	2
37	512
38	9216
39	43008
40	75264
41	56448
42	18816
43	2688
44	144
45	2
46	1024
47	23040
48	138240
49	322560
50	338688
51	169344

[2, 4, 2, 8, 12, 2, 16, 48, 24, 2, 32, 160, 160, 40, 2, 64, 480, 800, 400, 60, 2, 128, 1344, 3360, 2800, 840, 84, 2, 256, 3584, 12544, 15680, 7840, 1568, 112, 2, 512, 9216, 43008, 75264, 56448, 18816, 2688, 144, 2, 1024, 23040, 138240, 322560, 338688, 169344]

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