A251570 - cp's OEIS frontend

A251570 G.f. A(x) satisfies the condition that M(A(x)) is a power series in x consisting entirely of positive integer coefficients such that M(A(x) - x^k) has negative coefficients for k>0, where M(x) = 1 + xM(x) + xM(x)^2 is the g.f. of the Motzkin numbers A001006.

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

[1, 0, -1, -1, 1, 0, -1, -1, 0, 1, -1, 0, -1, -1, 0, -1, -1, -1, 0, -1, 0, -1, 0, 0, 0, -1, -1, -1, -1, 0, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, -1, 0, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, 0, -1, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, -1, -1, -1, 0, 0, -1, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, -1, 0, -1, 0, -1, -1, -1, -2, 0, 0, 0, 0, 0, 0, -1]

cp's OEIS Frontend

A251570 G.f. A(x) satisfies the condition that M(A(x)) is a power series in x consisting entirely of positive integer coefficients such that M(A(x) - x^k) has negative coefficients for k>0, where M(x) = 1 + xM(x) + xM(x)^2 is the g.f. of the Motzkin numbers A001006.

Table of values

List of values

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

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

cp's OEIS Frontend

A251570 G.f. A(x) satisfies the condition that M(A(x)) is a power series in x consisting entirely of positive integer coefficients such that M(A(x) - x^k) has negative coefficients for k>0, where M(x) = 1 + x*M(x) + x*M(x)^2 is the g.f. of the Motzkin numbers A001006.

Table of values

List of values

A251570 G.f. A(x) satisfies the condition that M(A(x)) is a power series in x consisting entirely of positive integer coefficients such that M(A(x) - x^k) has negative coefficients for k>0, where M(x) = 1 + xM(x) + xM(x)^2 is the g.f. of the Motzkin numbers A001006.

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