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A331988 Table T(n,k) read by antidiagonals. T(n,k) is the maximum value of Product_{i=1..n} Sum_{j=1..k} r_j[i] where each r_j is a permutation of {1..n}.

Table of values

n a(n)
1 1
2 2
3 2
4 6
5 9
6 3
7 24
8 64
9 20
10 4
11 120
12 625
13 216
14 36
15 5
16 720
17 7776
18 3136
19 512
20 56
21 6
22 5040
23 117649
24 59049
25 10000
26 1000
27 81
28 7
29 40320
30 2097152
31 1331000
32 248832
33 24336
34 1728
35 110
36 8
37 362880
38 43046721
39 35831808
40 7529536
41 759375
42 50625
43 2744
44 144
45 9
46 3628800
47 1000000000
48 1097199376
49 268435456
50 28652616
51 1889568
52 93636
53 4096
54 182
55 10

List of values

[1, 2, 2, 6, 9, 3, 24, 64, 20, 4, 120, 625, 216, 36, 5, 720, 7776, 3136, 512, 56, 6, 5040, 117649, 59049, 10000, 1000, 81, 7, 40320, 2097152, 1331000, 248832, 24336, 1728, 110, 8, 362880, 43046721, 35831808, 7529536, 759375, 50625, 2744, 144, 9, 3628800, 1000000000, 1097199376, 268435456, 28652616, 1889568, 93636, 4096, 182, 10]