A322215 - cp's OEIS frontend

A322215 G.f.: P(x,y) = Product_{n>=1} (1 - (x^n + y^n))^3, where P(x,y) = Sum_{n>=0} Sum_{k>=0} T(n,k) * x^n*y^k, as a square table of coefficients T(n,k) read by antidiagonals.

n	a(n)
0	1
1	-3
2	-3
3	0
4	6
5	0
6	5
7	6
8	6
9	5
10	0
11	-9
12	-12
13	-9
14	0
15	0
16	-9
17	-6
18	-6
19	-9
20	0
21	-7
22	-9
23	6
24	-6
25	6
26	-9
27	-7
28	0
29	12
30	12
31	27
32	27
33	12
34	12
35	0
36	0
37	12
38	24
39	30
40	6
41	30
42	24
43	12
44	0
45	0
46	12
47	-12
48	-23
49	-24
50	-24
51	-23
52	-12
53	12
54	0
55	9
56	12
57	0
58	3
59	-15
60	-12
61	-15
62	3
63	0
64	12
65	9
66	0
67	-15
68	-36
69	-54
70	-60
71	-60
72	-60
73	-60
74	-54
75	-36
76	-15
77	0
78	0
79	-15
80	-24
81	-23
82	-30
83	-9
84	-12
85	-9
86	-30
87	-23
88	-24
89	-15
90	0
91	0
92	-15
93	-6
94	-12
95	51
96	57
97	54
98	54
99	57
100	51
101	-12
102	-6
103	-15
104	0
105	0
106	-15
107	6
108	24
109	66
110	33
111	69
112	96
113	69
114	33
115	66
116	24
117	6
118	-15
119	0
120	-11
121	-15
122	24
123	49
124	87
125	69
126	127
127	93
128	93
129	127
130	69
131	87
132	49
133	24
134	-15
135	-11

[1, -3, -3, 0, 6, 0, 5, 6, 6, 5, 0, -9, -12, -9, 0, 0, -9, -6, -6, -9, 0, -7, -9, 6, -6, 6, -9, -7, 0, 12, 12, 27, 27, 12, 12, 0, 0, 12, 24, 30, 6, 30, 24, 12, 0, 0, 12, -12, -23, -24, -24, -23, -12, 12, 0, 9, 12, 0, 3, -15, -12, -15, 3, 0, 12, 9, 0, -15, -36, -54, -60, -60, -60, -60, -54, -36, -15, 0, 0, -15, -24, -23, -30, -9, -12, -9, -30, -23, -24, -15, 0, 0, -15, -6, -12, 51, 57, 54, 54, 57, 51, -12, -6, -15, 0, 0, -15, 6, 24, 66, 33, 69, 96, 69, 33, 66, 24, 6, -15, 0, -11, -15, 24, 49, 87, 69, 127, 93, 93, 127, 69, 87, 49, 24, -15, -11]

cp's OEIS Frontend

A322215 G.f.: P(x,y) = Product_{n>=1} (1 - (x^n + y^n))^3, where P(x,y) = Sum_{n>=0} Sum_{k>=0} T(n,k) * x^n*y^k, as a square table of coefficients T(n,k) read by antidiagonals.

Table of values

List of values

n	a(n)
0	1
1	-3
2	-3
3	0
4	6
5	0
6	5
7	6
8	6
9	5
10	0
11	-9
12	-12
13	-9
14	0
15	0
16	-9
17	-6
18	-6
19	-9
20	0
21	-7
22	-9
23	6
24	-6
25	6
26	-9
27	-7
28	0
29	12
30	12
31	27
32	27
33	12
34	12
35	0
36	0
37	12
38	24
39	30
40	6
41	30
42	24
43	12
44	0
45	0
46	12
47	-12
48	-23
49	-24
50	-24
51	-23
52	-12
53	12
54	0
55	9
56	12
57	0
58	3
59	-15
60	-12
61	-15
62	3
63	0
64	12
65	9
66	0
67	-15
68	-36
69	-54
70	-60
71	-60
72	-60
73	-60
74	-54
75	-36
76	-15
77	0
78	0
79	-15
80	-24
81	-23
82	-30
83	-9
84	-12
85	-9
86	-30
87	-23
88	-24
89	-15
90	0
91	0
92	-15
93	-6
94	-12
95	51
96	57
97	54
98	54
99	57
100	51
101	-12
102	-6
103	-15
104	0
105	0
106	-15
107	6
108	24
109	66
110	33
111	69
112	96
113	69
114	33
115	66
116	24
117	6
118	-15
119	0
120	-11
121	-15
122	24
123	49
124	87
125	69
126	127
127	93
128	93
129	127
130	69
131	87
132	49
133	24
134	-15
135	-11

n	a(n)
0	1
1	-3
2	-3
3	0
4	6
5	0
6	5
7	6
8	6
9	5
10	0
11	-9
12	-12
13	-9
14	0
15	0
16	-9
17	-6
18	-6
19	-9
20	0
21	-7
22	-9
23	6
24	-6
25	6
26	-9
27	-7
28	0
29	12
30	12
31	27
32	27
33	12
34	12
35	0
36	0
37	12
38	24
39	30
40	6
41	30
42	24
43	12
44	0
45	0
46	12
47	-12
48	-23
49	-24
50	-24
51	-23
52	-12
53	12
54	0
55	9
56	12
57	0
58	3
59	-15
60	-12
61	-15
62	3
63	0
64	12
65	9
66	0
67	-15
68	-36
69	-54
70	-60
71	-60
72	-60
73	-60
74	-54
75	-36
76	-15
77	0
78	0
79	-15
80	-24
81	-23
82	-30
83	-9
84	-12
85	-9
86	-30
87	-23
88	-24
89	-15
90	0
91	0
92	-15
93	-6
94	-12
95	51
96	57
97	54
98	54
99	57
100	51
101	-12
102	-6
103	-15
104	0
105	0
106	-15
107	6
108	24
109	66
110	33
111	69
112	96
113	69
114	33
115	66
116	24
117	6
118	-15
119	0
120	-11
121	-15
122	24
123	49
124	87
125	69
126	127
127	93
128	93
129	127
130	69
131	87
132	49
133	24
134	-15
135	-11

n	a(n)
0	1
1	-3
2	-3
3	0
4	6
5	0
6	5
7	6
8	6
9	5
10	0
11	-9
12	-12
13	-9
14	0
15	0
16	-9
17	-6
18	-6
19	-9
20	0
21	-7
22	-9
23	6
24	-6
25	6
26	-9
27	-7
28	0
29	12
30	12
31	27
32	27
33	12
34	12
35	0
36	0
37	12
38	24
39	30
40	6
41	30
42	24
43	12
44	0
45	0
46	12
47	-12
48	-23
49	-24
50	-24
51	-23
52	-12
53	12
54	0
55	9
56	12
57	0
58	3
59	-15
60	-12
61	-15
62	3
63	0
64	12
65	9
66	0
67	-15
68	-36
69	-54
70	-60
71	-60
72	-60
73	-60
74	-54
75	-36
76	-15
77	0
78	0
79	-15
80	-24
81	-23
82	-30
83	-9
84	-12
85	-9
86	-30
87	-23
88	-24
89	-15
90	0
91	0
92	-15
93	-6
94	-12
95	51
96	57
97	54
98	54
99	57
100	51
101	-12
102	-6
103	-15
104	0
105	0
106	-15
107	6
108	24
109	66
110	33
111	69
112	96
113	69
114	33
115	66
116	24
117	6
118	-15
119	0
120	-11
121	-15
122	24
123	49
124	87
125	69
126	127
127	93
128	93
129	127
130	69
131	87
132	49
133	24
134	-15
135	-11