A125181 - cp's OEIS frontend

A125181 Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n whose ascent lengths form the k-th partition of the integer n; the partitions of n are ordered in the "Mathematica" ordering.

n	a(n)
1	1
2	1
3	1
4	1
5	3
6	1
7	1
8	4
9	2
10	6
11	1
12	1
13	5
14	5
15	10
16	10
17	10
18	1
19	1
20	6
21	6
22	15
23	3
24	30
25	20
26	5
27	30
28	15
29	1
30	1
31	7
32	7
33	21
34	7
35	42
36	35
37	21
38	21
39	105
40	35
41	35
42	70
43	21
44	1
45	1
46	8
47	8
48	28
49	8
50	56
51	56
52	4
53	56
54	28
55	168
56	70
57	28
58	84
59	168
60	280
61	56
62	14
63	140
64	140
65	28
66	1
67	1
68	9
69	9
70	36
71	9
72	72
73	84
74	9
75	72
76	36
77	252
78	126
79	36

[1, 1, 1, 1, 3, 1, 1, 4, 2, 6, 1, 1, 5, 5, 10, 10, 10, 1, 1, 6, 6, 15, 3, 30, 20, 5, 30, 15, 1, 1, 7, 7, 21, 7, 42, 35, 21, 21, 105, 35, 35, 70, 21, 1, 1, 8, 8, 28, 8, 56, 56, 4, 56, 28, 168, 70, 28, 84, 168, 280, 56, 14, 140, 140, 28, 1, 1, 9, 9, 36, 9, 72, 84, 9, 72, 36, 252, 126, 36]

cp's OEIS Frontend

A125181 Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n whose ascent lengths form the k-th partition of the integer n; the partitions of n are ordered in the "Mathematica" ordering.

Table of values

List of values

n	a(n)
1	1
2	1
3	1
4	1
5	3
6	1
7	1
8	4
9	2
10	6
11	1
12	1
13	5
14	5
15	10
16	10
17	10
18	1
19	1
20	6
21	6
22	15
23	3
24	30
25	20
26	5
27	30
28	15
29	1
30	1
31	7
32	7
33	21
34	7
35	42
36	35
37	21
38	21
39	105
40	35
41	35
42	70
43	21
44	1
45	1
46	8
47	8
48	28
49	8
50	56
51	56
52	4
53	56
54	28
55	168
56	70
57	28
58	84
59	168
60	280
61	56
62	14
63	140
64	140
65	28
66	1
67	1
68	9
69	9
70	36
71	9
72	72
73	84
74	9
75	72
76	36
77	252
78	126
79	36

n	a(n)
1	1
2	1
3	1
4	1
5	3
6	1
7	1
8	4
9	2
10	6
11	1
12	1
13	5
14	5
15	10
16	10
17	10
18	1
19	1
20	6
21	6
22	15
23	3
24	30
25	20
26	5
27	30
28	15
29	1
30	1
31	7
32	7
33	21
34	7
35	42
36	35
37	21
38	21
39	105
40	35
41	35
42	70
43	21
44	1
45	1
46	8
47	8
48	28
49	8
50	56
51	56
52	4
53	56
54	28
55	168
56	70
57	28
58	84
59	168
60	280
61	56
62	14
63	140
64	140
65	28
66	1
67	1
68	9
69	9
70	36
71	9
72	72
73	84
74	9
75	72
76	36
77	252
78	126
79	36

n	a(n)
1	1
2	1
3	1
4	1
5	3
6	1
7	1
8	4
9	2
10	6
11	1
12	1
13	5
14	5
15	10
16	10
17	10
18	1
19	1
20	6
21	6
22	15
23	3
24	30
25	20
26	5
27	30
28	15
29	1
30	1
31	7
32	7
33	21
34	7
35	42
36	35
37	21
38	21
39	105
40	35
41	35
42	70
43	21
44	1
45	1
46	8
47	8
48	28
49	8
50	56
51	56
52	4
53	56
54	28
55	168
56	70
57	28
58	84
59	168
60	280
61	56
62	14
63	140
64	140
65	28
66	1
67	1
68	9
69	9
70	36
71	9
72	72
73	84
74	9
75	72
76	36
77	252
78	126
79	36