A111177 Number of base n numbers in which each digit appears at most once (all unnecessary 0's deleted).

4, 21, 130, 913, 7176, 62629, 602806, 6356865, 72994348, 907497301, 12152572554, 174476220241, 2674434002800, 43603430324133, 753581024080126, 13763517571878529, 264919276238885076, 5360264479811601685

Offset

2,1

Comments

Finite expansions after the "decimal" point are allowed, but there must be a number before it (so we can have 0.1, but not .01).

Links

Table of n, a(n) for n=2..19.

Cf. A001339.

Formula

a(n)=Sum(i=0, n-1) (i^2+i+1)(n-1)!/(n-1-i)!; n>1

Example

a(2)=4 because in the binary system only the numbers 0; 1; 0.1; 10 can be written with each digit used at most once (all unnecessary 0's deleted).

Mathematica

f[n_] := Sum[(i^2 + i + 1)(n - 1)!/(n - 1 - i)!, {i, 0, n - 1}]; Table[ f[n], {n, 2, 19}] (* Robert G. Wilson v *)

Crossrefs

Sequence in context: A300674 A232956 A234268 * A141052 A058308 A078591

Adjacent sequences: A111174 A111175 A111176 * A111178 A111179 A111180

Keyword

nonn,base

Author

Rafael Hofman (mathematics287(AT)yahoo.de), Oct 22 2005

Extensions

More terms from Robert G. Wilson v, Oct 29 2005

Status

approved