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EXAMPLE
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The first terms in base 10 and factorial base, alongside their partial sums in factorial base, are:
n a(n) a(n) in fact. base Partial sum in fact. base
-- --------- --------------------- -------------------------
1 1 1 1
2 2 1,0 1,1
3 6 1,0,0 1,1,1
4 8 1,1,0 2,2,1
5 24 1,0,0,0 1,2,2,1
6 30 1,1,0,0 2,3,2,1
7 48 2,0,0,0 4,3,2,1
8 120 1,0,0,0,0 1,4,3,2,1
9 240 2,0,0,0,0 3,4,3,2,1
10 720 1,0,0,0,0,0 1,3,4,3,2,1
11 840 1,1,0,0,0,0 2,4,4,3,2,1
12 1440 2,0,0,0,0,0 4,4,4,3,2,1
13 1560 2,1,0,0,0,0 6,5,4,3,2,1
14 5040 1,0,0,0,0,0,0 1,6,5,4,3,2,1
15 10080 2,0,0,0,0,0,0 3,6,5,4,3,2,1
16 15120 3,0,0,0,0,0,0 6,6,5,4,3,2,1
17 40320 1,0,0,0,0,0,0,0 1,6,6,5,4,3,2,1
18 45360 1,1,0,0,0,0,0,0 2,7,6,5,4,3,2,1
19 80640 2,0,0,0,0,0,0,0 4,7,6,5,4,3,2,1
20 120960 3,0,0,0,0,0,0,0 7,7,6,5,4,3,2,1
21 362880 1,0,0,0,0,0,0,0,0 1,7,7,6,5,4,3,2,1
22 403200 1,1,0,0,0,0,0,0,0 2,8,7,6,5,4,3,2,1
23 725760 2,0,0,0,0,0,0,0,0 4,8,7,6,5,4,3,2,1
24 1088640 3,0,0,0,0,0,0,0,0 7,8,7,6,5,4,3,2,1
25 3628800 1,0,0,0,0,0,0,0,0,0 1,7,8,7,6,5,4,3,2,1
26 3991680 1,1,0,0,0,0,0,0,0,0 2,8,8,7,6,5,4,3,2,1
27 7257600 2,0,0,0,0,0,0,0,0,0 4,8,8,7,6,5,4,3,2,1
28 7620480 2,1,0,0,0,0,0,0,0,0 6,9,8,7,6,5,4,3,2,1
29 10886400 3,0,0,0,0,0,0,0,0,0 9,9,8,7,6,5,4,3,2,1
30 39916800 1,0,0,0,0,0,0,0,0,0,0 1,9,9,8,7,6,5,4,3,2,1
31 43545600 1,1,0,0,0,0,0,0,0,0,0 2,10,9,8,7,6,5,4,3,2,1
32 79833600 2,0,0,0,0,0,0,0,0,0,0 4,10,9,8,7,6,5,4,3,2,1
33 119750400 3,0,0,0,0,0,0,0,0,0,0 7,10,9,8,7,6,5,4,3,2,1
34 159667200 4,0,0,0,0,0,0,0,0,0,0 11,10,9,8,7,6,5,4,3,2,1
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