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A137634 Square array where T(n,k) = Sum_{j=0..k} C(n+2*j,j)*C(n+2*j,k-j), read by antidiagonals.

Table of values

n a(n)
0 1
1 1
2 2
3 1
4 4
5 10
6 1
7 6
8 19
9 46
10 1
11 8
12 32
13 94
14 226
15 1
16 10
17 49
18 170
19 474
20 1136
21 1
22 12
23 70
24 282
25 899
26 2431
27 5810
28 1
29 14
30 95
31 438
32 1577
33 4764
34 12609
35 30080
36 1
37 16
38 124
39 646
40 2600
41 8701
42 25318
43 65972
44 157162
45 1
46 18
47 157
48 914
49 4076
50 15000
51 47682
52 134964
53 347524
54 826992

List of values

[1, 1, 2, 1, 4, 10, 1, 6, 19, 46, 1, 8, 32, 94, 226, 1, 10, 49, 170, 474, 1136, 1, 12, 70, 282, 899, 2431, 5810, 1, 14, 95, 438, 1577, 4764, 12609, 30080, 1, 16, 124, 646, 2600, 8701, 25318, 65972, 157162, 1, 18, 157, 914, 4076, 15000, 47682, 134964, 347524, 826992]