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A344503 as a simple table

na(n)
01
10
2-1
33
40
5-5
615
70
8-28
984
100
11-165
12495
130
14-1001
153003
160
17-6188
1818564
190
20-38760
21116280
220
23-245157
24735471
250
26-1562275
274686825
280
29-10015005
3030045015
310
32-64512240
33193536720
340
35-417225900
361251677700
370
38-2707475148
398122425444
400
41-17620076360

[1,0,-1,3,0,-5,15,0,-28,84,0,-165,495,0,-1001,
 3003,0,-6188,18564,0,-38760,116280,0,-245157,
 735471,0,-1562275,4686825,0,-10015005,30045015,0,
 -64512240,193536720,0,-417225900,1251677700,0,
 -2707475148,8122425444,0,-17620076360]