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A344110 as a simple table

na(n)
01
11
22
31
44
516
61
78
864
9512
101
1116
12256
134096
1465536
151
1632
171024
1832768
191048576
2033554432
211
2264
234096
24262144
2516777216
261073741824
2768719476736
281
29128
3016384
312097152
32268435456
3334359738368
344398046511104
35562949953421312

[1,1,2,1,4,16,1,8,64,512,1,16,256,4096,65536,1,32,
 1024,32768,1048576,33554432,1,64,4096,262144,
 16777216,1073741824,68719476736,1,128,16384,
 2097152,268435456,34359738368,4398046511104,
 562949953421312]