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A199660 as a simple table

na(n)
01
11
22
31
45
52
620
76
8114
924
10864
11120
128280
13720
1496480
155040
161325520
1740320
1820966400
19362880
20374855040
213628800
227468070400
2339916800
24163938297600
25479001600
263929729126400
276227020800
28102104460057600
2987178291200
302857878742118400
311307674368000

[1,1,2,1,5,2,20,6,114,24,864,120,8280,720,96480,
 5040,1325520,40320,20966400,362880,374855040,
 3628800,7468070400,39916800,163938297600,
 479001600,3929729126400,6227020800,
 102104460057600,87178291200,2857878742118400,
 1307674368000]