A129176 - cp's OEIS frontend

A129176 Irregular triangle read by rows: T(n,k) is the number of Dyck words of length 2n having k inversions (n >= 0, k >= 0).

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	2
7	1
8	1
9	1
10	2
11	3
12	3
13	3
14	1
15	1
16	1
17	2
18	3
19	5
20	5
21	7
22	7
23	6
24	4
25	1
26	1
27	1
28	2
29	3
30	5
31	7
32	9
33	11
34	14
35	16
36	16
37	17
38	14
39	10
40	5
41	1
42	1
43	1
44	2
45	3
46	5
47	7
48	11
49	13
50	18
51	22
52	28
53	32
54	37
55	40
56	44
57	43
58	40
59	35
60	25
61	15
62	6
63	1
64	1
65	1
66	2
67	3
68	5
69	7
70	11
71	15
72	20
73	26
74	34
75	42
76	53
77	63
78	73
79	85
80	96
81	106
82	113
83	118
84	118
85	115
86	102
87	86
88	65
89	41
90	21
91	7
92	1

[1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 3, 3, 1, 1, 1, 2, 3, 5, 5, 7, 7, 6, 4, 1, 1, 1, 2, 3, 5, 7, 9, 11, 14, 16, 16, 17, 14, 10, 5, 1, 1, 1, 2, 3, 5, 7, 11, 13, 18, 22, 28, 32, 37, 40, 44, 43, 40, 35, 25, 15, 6, 1, 1, 1, 2, 3, 5, 7, 11, 15, 20, 26, 34, 42, 53, 63, 73, 85, 96, 106, 113, 118, 118, 115, 102, 86, 65, 41, 21, 7, 1]

cp's OEIS Frontend

A129176 Irregular triangle read by rows: T(n,k) is the number of Dyck words of length 2n having k inversions (n >= 0, k >= 0).

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	2
7	1
8	1
9	1
10	2
11	3
12	3
13	3
14	1
15	1
16	1
17	2
18	3
19	5
20	5
21	7
22	7
23	6
24	4
25	1
26	1
27	1
28	2
29	3
30	5
31	7
32	9
33	11
34	14
35	16
36	16
37	17
38	14
39	10
40	5
41	1
42	1
43	1
44	2
45	3
46	5
47	7
48	11
49	13
50	18
51	22
52	28
53	32
54	37
55	40
56	44
57	43
58	40
59	35
60	25
61	15
62	6
63	1
64	1
65	1
66	2
67	3
68	5
69	7
70	11
71	15
72	20
73	26
74	34
75	42
76	53
77	63
78	73
79	85
80	96
81	106
82	113
83	118
84	118
85	115
86	102
87	86
88	65
89	41
90	21
91	7
92	1

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	2
7	1
8	1
9	1
10	2
11	3
12	3
13	3
14	1
15	1
16	1
17	2
18	3
19	5
20	5
21	7
22	7
23	6
24	4
25	1
26	1
27	1
28	2
29	3
30	5
31	7
32	9
33	11
34	14
35	16
36	16
37	17
38	14
39	10
40	5
41	1
42	1
43	1
44	2
45	3
46	5
47	7
48	11
49	13
50	18
51	22
52	28
53	32
54	37
55	40
56	44
57	43
58	40
59	35
60	25
61	15
62	6
63	1
64	1
65	1
66	2
67	3
68	5
69	7
70	11
71	15
72	20
73	26
74	34
75	42
76	53
77	63
78	73
79	85
80	96
81	106
82	113
83	118
84	118
85	115
86	102
87	86
88	65
89	41
90	21
91	7
92	1

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	2
7	1
8	1
9	1
10	2
11	3
12	3
13	3
14	1
15	1
16	1
17	2
18	3
19	5
20	5
21	7
22	7
23	6
24	4
25	1
26	1
27	1
28	2
29	3
30	5
31	7
32	9
33	11
34	14
35	16
36	16
37	17
38	14
39	10
40	5
41	1
42	1
43	1
44	2
45	3
46	5
47	7
48	11
49	13
50	18
51	22
52	28
53	32
54	37
55	40
56	44
57	43
58	40
59	35
60	25
61	15
62	6
63	1
64	1
65	1
66	2
67	3
68	5
69	7
70	11
71	15
72	20
73	26
74	34
75	42
76	53
77	63
78	73
79	85
80	96
81	106
82	113
83	118
84	118
85	115
86	102
87	86
88	65
89	41
90	21
91	7
92	1