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A101981 as a simple table

na(n)
00
11
2-1
34
4-33
5456
6-9460
7274800
8-10643745
9530052880
10-32995478376
112510382661920
12-229195817258100
1324730000147369440
14-3113066087894608560
15452168671458789789504
16-75059305956331837485345
1714121026957032156557396000
18-2988687741694684876495689040

[0,1,-1,4,-33,456,-9460,274800,-10643745,
 530052880,-32995478376,2510382661920,
 -229195817258100,24730000147369440,
 -3113066087894608560,452168671458789789504,
 -75059305956331837485345,
 14121026957032156557396000,
 -2988687741694684876495689040]