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A117972 as a simple table

na(n)
01
1-1
23
3-45
4315
5-14175
6467775
7-42567525
8638512875
9-97692469875
109280784638125
11-2143861251406875
12147926426347074375
13-48076088562799171875
149086380738369043484375
15-3952575621190533915703125

[1,-1,3,-45,315,-14175,467775,-42567525,638512875,
 -97692469875,9280784638125,-2143861251406875,
 147926426347074375,-48076088562799171875,
 9086380738369043484375,-3952575621190533915703125]