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A290776 Triangle T(n,k) read by rows: the number of connected, loopless, non-oriented, vertex-labeled graphs with n >= 0 edges and k >= 1 vertices, allowing multi-edges.

Table of values

n a(n)
0 1
1 0
2 1
3 0
4 1
5 3
6 0
7 1
8 7
9 16
10 0
11 1
12 12
13 63
14 125
15 0
16 1
17 18
18 162
19 722
20 1296
21 0
22 1
23 25
24 341
25 2565
26 10140
27 16807
28 0
29 1
30 33
31 636
32 7180
33 47100
34 169137
35 262144
36 0
37 1
38 42
39 1092
40 17335
41 168285
42 987567
43 3271576
44 4782969
45 0
46 1
47 52
48 1764
49 37750
50 509545
51 4364017
52 23315936
53 72043092
54 100000000

List of values

[1, 0, 1, 0, 1, 3, 0, 1, 7, 16, 0, 1, 12, 63, 125, 0, 1, 18, 162, 722, 1296, 0, 1, 25, 341, 2565, 10140, 16807, 0, 1, 33, 636, 7180, 47100, 169137, 262144, 0, 1, 42, 1092, 17335, 168285, 987567, 3271576, 4782969, 0, 1, 52, 1764, 37750, 509545, 4364017, 23315936, 72043092, 100000000]