A327031 - cp's OEIS frontend

A327031 A(n, k) = Sum_{d|n} phi(d)*T(n/d, k) if n > 0 and A(0, k) = 0 where T(n, k) = binomial(n+k-1, n). Square array read by ascending antidiagonals, with n, k >= 0.

n	a(n)
0	0
1	0
2	0
3	0
4	1
5	0
6	0
7	2
8	2
9	0
10	0
11	3
12	5
13	3
14	0
15	0
16	4
17	8
18	9
19	4
20	0
21	0
22	5
23	12
24	16
25	14
26	5
27	0
28	0
29	6
30	14
31	27
32	28
33	20
34	6
35	0
36	0
37	7
38	21
39	33
40	53
41	45
42	27
43	7
44	0
45	0
46	8
47	20
48	56
49	72
50	95
51	68
52	35
53	8
54	0
55	0
56	9
57	28
58	54
59	132
60	146
61	159
62	98
63	44
64	9
65	0
66	0
67	10
68	30
69	84
70	144
71	285
72	276
73	252
74	136
75	54
76	10
77	0

[0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 5, 3, 0, 0, 4, 8, 9, 4, 0, 0, 5, 12, 16, 14, 5, 0, 0, 6, 14, 27, 28, 20, 6, 0, 0, 7, 21, 33, 53, 45, 27, 7, 0, 0, 8, 20, 56, 72, 95, 68, 35, 8, 0, 0, 9, 28, 54, 132, 146, 159, 98, 44, 9, 0, 0, 10, 30, 84, 144, 285, 276, 252, 136, 54, 10, 0]

cp's OEIS Frontend

A327031 A(n, k) = Sum_{d|n} phi(d)*T(n/d, k) if n > 0 and A(0, k) = 0 where T(n, k) = binomial(n+k-1, n). Square array read by ascending antidiagonals, with n, k >= 0.

Table of values

List of values

n	a(n)
0	0
1	0
2	0
3	0
4	1
5	0
6	0
7	2
8	2
9	0
10	0
11	3
12	5
13	3
14	0
15	0
16	4
17	8
18	9
19	4
20	0
21	0
22	5
23	12
24	16
25	14
26	5
27	0
28	0
29	6
30	14
31	27
32	28
33	20
34	6
35	0
36	0
37	7
38	21
39	33
40	53
41	45
42	27
43	7
44	0
45	0
46	8
47	20
48	56
49	72
50	95
51	68
52	35
53	8
54	0
55	0
56	9
57	28
58	54
59	132
60	146
61	159
62	98
63	44
64	9
65	0
66	0
67	10
68	30
69	84
70	144
71	285
72	276
73	252
74	136
75	54
76	10
77	0

n	a(n)
0	0
1	0
2	0
3	0
4	1
5	0
6	0
7	2
8	2
9	0
10	0
11	3
12	5
13	3
14	0
15	0
16	4
17	8
18	9
19	4
20	0
21	0
22	5
23	12
24	16
25	14
26	5
27	0
28	0
29	6
30	14
31	27
32	28
33	20
34	6
35	0
36	0
37	7
38	21
39	33
40	53
41	45
42	27
43	7
44	0
45	0
46	8
47	20
48	56
49	72
50	95
51	68
52	35
53	8
54	0
55	0
56	9
57	28
58	54
59	132
60	146
61	159
62	98
63	44
64	9
65	0
66	0
67	10
68	30
69	84
70	144
71	285
72	276
73	252
74	136
75	54
76	10
77	0

n	a(n)
0	0
1	0
2	0
3	0
4	1
5	0
6	0
7	2
8	2
9	0
10	0
11	3
12	5
13	3
14	0
15	0
16	4
17	8
18	9
19	4
20	0
21	0
22	5
23	12
24	16
25	14
26	5
27	0
28	0
29	6
30	14
31	27
32	28
33	20
34	6
35	0
36	0
37	7
38	21
39	33
40	53
41	45
42	27
43	7
44	0
45	0
46	8
47	20
48	56
49	72
50	95
51	68
52	35
53	8
54	0
55	0
56	9
57	28
58	54
59	132
60	146
61	159
62	98
63	44
64	9
65	0
66	0
67	10
68	30
69	84
70	144
71	285
72	276
73	252
74	136
75	54
76	10
77	0