[lruunnwl] permutations of subsets

f(n) = sum(k=0, n, binomial(n,k) * k!)

for(i=0, 12, x=f(i); print(i" "x" ",x-1))

0 1 0
1 2 1
2 5 4
3 16 15
4 65 64
5 326 325
6 1957 1956
7 13700 13699
8 109601 109600
9 986410 986409
10 9864101 9864100
11 108505112 108505111
12 1302061345 1302061344

OEIS A000522

the sequence grows quickly, conjecturally asymptotically factorial(n) * e .

permutations of subsets of 4 physical items is intriguing: 64 possibilities excluding empty set, encoding exactly 6 bits.  base64.  the empty subset can be used as a separator.

5 physical items encodes 1 byte with room for escape characters.

"physical" items because duplication forbidden.  if repetitions permitted, then future post ijyxrmio .

inspired by My Little Pony action figures arranged in a row.