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A119830 Bi-diagonal inverse of (2n)!/(2k)!.

Table of values

n a(n)
0 1
1 -2
2 1
3 0
4 -12
5 1
6 0
7 0
8 -30
9 1
10 0
11 0
12 0
13 -56
14 1
15 0
16 0
17 0
18 0
19 -90
20 1
21 0
22 0
23 0
24 0
25 0
26 -132
27 1
28 0
29 0
30 0
31 0
32 0
33 0
34 -182
35 1
36 0
37 0
38 0
39 0
40 0
41 0
42 0
43 -240
44 1
45 0
46 0
47 0
48 0
49 0
50 0
51 0
52 0
53 -306
54 1
55 0
56 0
57 0
58 0
59 0
60 0
61 0
62 0
63 0
64 -380
65 1
66 0
67 0
68 0
69 0
70 0
71 0
72 0
73 0
74 0
75 0
76 -462
77 1
78 0
79 0
80 0
81 0
82 0
83 0
84 0
85 0
86 0
87 0
88 0
89 -552
90 1
91 0
92 0
93 0
94 0
95 0
96 0

List of values

[1, -2, 1, 0, -12, 1, 0, 0, -30, 1, 0, 0, 0, -56, 1, 0, 0, 0, 0, -90, 1, 0, 0, 0, 0, 0, -132, 1, 0, 0, 0, 0, 0, 0, -182, 1, 0, 0, 0, 0, 0, 0, 0, -240, 1, 0, 0, 0, 0, 0, 0, 0, 0, -306, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -380, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -462, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -552, 1, 0, 0, 0, 0, 0, 0]