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A119328 Number triangle T(n,k)=sum{i=0..n, (-1)^(n-i)*C(n,i)*sum{j=0..i-k, C(k,2j)*C(i-k,2j)}}.

Table of values

n a(n)
0 1
1 0
2 1
3 0
4 -1
5 1
6 0
7 1
8 -2
9 1
10 0
11 -1
12 4
13 -3
14 1
15 0
16 1
17 -6
18 9
19 -4
20 1
21 0
22 -1
23 8
24 -19
25 16
26 -5
27 1
28 0
29 1
30 -10
31 33
32 -44
33 25
34 -6
35 1
36 0
37 -1
38 12
39 -51
40 96
41 -85
42 36
43 -7
44 1
45 0
46 1
47 -14
48 73
49 -180
50 225
51 -146
52 49
53 -8
54 1
55 0
56 -1
57 16
58 -99
59 304
60 -501
61 456
62 -231
63 64
64 -9
65 1

List of values

[1, 0, 1, 0, -1, 1, 0, 1, -2, 1, 0, -1, 4, -3, 1, 0, 1, -6, 9, -4, 1, 0, -1, 8, -19, 16, -5, 1, 0, 1, -10, 33, -44, 25, -6, 1, 0, -1, 12, -51, 96, -85, 36, -7, 1, 0, 1, -14, 73, -180, 225, -146, 49, -8, 1, 0, -1, 16, -99, 304, -501, 456, -231, 64, -9, 1]