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A109591 as a simple table

na(n)
00
1-3
22
33
456
5-360
612420
7-303030
810226880
9-381416040
1016356484800
11-781899663600
1241374146038400
13-2397894225620400
14151087293619567200
15-10281399143079546000
16751437976013183232000
17-58702720576973120928000
184881171236699697126048000

[0,-3,2,3,56,-360,12420,-303030,10226880,
 -381416040,16356484800,-781899663600,
 41374146038400,-2397894225620400,
 151087293619567200,-10281399143079546000,
 751437976013183232000,-58702720576973120928000,
 4881171236699697126048000]