A191395 - cp's OEIS frontend

A191395 Triangle read by rows: T(n,k) is the number of dispersed Dyck paths of length n (i.e., of Motzkin paths of length n with no (1,0)-steps at positive heights) for which the sum of the heights of its base pyramid is k. A base pyramid is a factor of the form U^j D^j (j>0), starting at the horizontal axis. Here U=(1,1) and D=(1,-1).

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	1
7	3
8	2
9	1
10	4
11	5
12	2
13	5
14	9
15	4
16	3
17	6
18	14
19	12
20	8
21	9
22	20
23	25
24	8
25	13
26	14
27	27
28	44
29	28
30	31
31	29
32	40
33	70
34	66
35	16
36	49
37	54
38	62
39	104
40	129
41	64
42	109
43	115
44	116
45	159
46	225
47	168
48	32
49	170
50	212
51	217
52	250
53	363
54	360
55	144
56	371
57	430
58	445
59	444
60	581
61	681
62	416
63	64
64	581
65	772
66	854
67	820
68	938
69	1182
70	968
71	320

[1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 4, 5, 2, 5, 9, 4, 3, 6, 14, 12, 8, 9, 20, 25, 8, 13, 14, 27, 44, 28, 31, 29, 40, 70, 66, 16, 49, 54, 62, 104, 129, 64, 109, 115, 116, 159, 225, 168, 32, 170, 212, 217, 250, 363, 360, 144, 371, 430, 445, 444, 581, 681, 416, 64, 581, 772, 854, 820, 938, 1182, 968, 320]

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