A337126 - cp's OEIS frontend

A337126 Irregular triangular array read by rows. T(n,k) is the number of permutations of {1,2,...,n} with descent set {1,3,5,...,m} (where m is the greatest odd integer less than n) that have exactly k inversions, n=0, k=0, or n>0, 0<=k<=ceiling((n-1)^2/2).

n	a(n)
0	1
1	1
2	0
3	1
4	0
5	1
6	1
7	0
8	0
9	1
10	1
11	2
12	1
13	0
14	0
15	1
16	2
17	3
18	4
19	3
20	2
21	1
22	0
23	0
24	0
25	1
26	2
27	5
28	7
29	9
30	10
31	10
32	8
33	5
34	3
35	1
36	0
37	0
38	0
39	1
40	3
41	7
42	13
43	19
44	26
45	32
46	35
47	35
48	32
49	26
50	19
51	13
52	7
53	3
54	1
55	0
56	0
57	0
58	0
59	1
60	3
61	9
62	18
63	32
64	50
65	72
66	95
67	117
68	134
69	143
70	145
71	138
72	122
73	101
74	78
75	55
76	36
77	21
78	10
79	4
80	1

[1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 0, 1, 2, 5, 7, 9, 10, 10, 8, 5, 3, 1, 0, 0, 0, 1, 3, 7, 13, 19, 26, 32, 35, 35, 32, 26, 19, 13, 7, 3, 1, 0, 0, 0, 0, 1, 3, 9, 18, 32, 50, 72, 95, 117, 134, 143, 145, 138, 122, 101, 78, 55, 36, 21, 10, 4, 1]

cp's OEIS Frontend

A337126 Irregular triangular array read by rows. T(n,k) is the number of permutations of {1,2,...,n} with descent set {1,3,5,...,m} (where m is the greatest odd integer less than n) that have exactly k inversions, n=0, k=0, or n>0, 0<=k<=ceiling((n-1)^2/2).

Table of values

List of values

n	a(n)
0	1
1	1
2	0
3	1
4	0
5	1
6	1
7	0
8	0
9	1
10	1
11	2
12	1
13	0
14	0
15	1
16	2
17	3
18	4
19	3
20	2
21	1
22	0
23	0
24	0
25	1
26	2
27	5
28	7
29	9
30	10
31	10
32	8
33	5
34	3
35	1
36	0
37	0
38	0
39	1
40	3
41	7
42	13
43	19
44	26
45	32
46	35
47	35
48	32
49	26
50	19
51	13
52	7
53	3
54	1
55	0
56	0
57	0
58	0
59	1
60	3
61	9
62	18
63	32
64	50
65	72
66	95
67	117
68	134
69	143
70	145
71	138
72	122
73	101
74	78
75	55
76	36
77	21
78	10
79	4
80	1

n	a(n)
0	1
1	1
2	0
3	1
4	0
5	1
6	1
7	0
8	0
9	1
10	1
11	2
12	1
13	0
14	0
15	1
16	2
17	3
18	4
19	3
20	2
21	1
22	0
23	0
24	0
25	1
26	2
27	5
28	7
29	9
30	10
31	10
32	8
33	5
34	3
35	1
36	0
37	0
38	0
39	1
40	3
41	7
42	13
43	19
44	26
45	32
46	35
47	35
48	32
49	26
50	19
51	13
52	7
53	3
54	1
55	0
56	0
57	0
58	0
59	1
60	3
61	9
62	18
63	32
64	50
65	72
66	95
67	117
68	134
69	143
70	145
71	138
72	122
73	101
74	78
75	55
76	36
77	21
78	10
79	4
80	1

n	a(n)
0	1
1	1
2	0
3	1
4	0
5	1
6	1
7	0
8	0
9	1
10	1
11	2
12	1
13	0
14	0
15	1
16	2
17	3
18	4
19	3
20	2
21	1
22	0
23	0
24	0
25	1
26	2
27	5
28	7
29	9
30	10
31	10
32	8
33	5
34	3
35	1
36	0
37	0
38	0
39	1
40	3
41	7
42	13
43	19
44	26
45	32
46	35
47	35
48	32
49	26
50	19
51	13
52	7
53	3
54	1
55	0
56	0
57	0
58	0
59	1
60	3
61	9
62	18
63	32
64	50
65	72
66	95
67	117
68	134
69	143
70	145
71	138
72	122
73	101
74	78
75	55
76	36
77	21
78	10
79	4
80	1