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A123361 as a simple table

na(n)
01
11
21
32
41
5-1
66
71
8-4
91
1024
11-2
12-17
138
14-1
15120
16-34
17-83
1857
19-13
201
21720
22-324
23-464
24425
25-135
2619
27-1
285040
29-2988
30-2924
313439
32-1370
33268
34-26
351
3640320
37-28944
38-20404
3930436
40-14399
413514
42-476
4334
44-1
45362880
46-300816
47-154692
48294328
49-160027
5046025
51-7798
52782
53-43
541

[1,1,1,2,1,-1,6,1,-4,1,24,-2,-17,8,-1,120,-34,-83,
 57,-13,1,720,-324,-464,425,-135,19,-1,5040,-2988,
 -2924,3439,-1370,268,-26,1,40320,-28944,-20404,
 30436,-14399,3514,-476,34,-1,362880,-300816,
 -154692,294328,-160027,46025,-7798,782,-43,1]