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A133815 Square array of Hankel transforms of binomial(n+k,floor((n+k)/2)), read by antidiagonals.

Table of values

n a(n)
0 1
1 1
2 1
3 1
4 1
5 1
6 1
7 -1
8 2
9 1
10 1
11 -1
12 3
13 3
14 1
15 1
16 1
17 4
18 -6
19 6
20 1
21 1
22 1
23 5
24 -10
25 20
26 10
27 1
28 1
29 -1
30 6
31 15
32 50
33 -50
34 20
35 1
36 1
37 -1
38 7
39 21
40 105
41 -175
42 175
43 35
44 1
45 1
46 1
47 8
48 -28
49 196
50 490
51 980
52 -490
53 70
54 1
55 1
56 1
57 9
58 -36
59 336
60 1176
61 4116
62 -4116
63 1764
64 126
65 1

List of values

[1, 1, 1, 1, 1, 1, 1, -1, 2, 1, 1, -1, 3, 3, 1, 1, 1, 4, -6, 6, 1, 1, 1, 5, -10, 20, 10, 1, 1, -1, 6, 15, 50, -50, 20, 1, 1, -1, 7, 21, 105, -175, 175, 35, 1, 1, 1, 8, -28, 196, 490, 980, -490, 70, 1, 1, 1, 9, -36, 336, 1176, 4116, -4116, 1764, 126, 1]