A036918 a(n) = floor(e*(n-1)*(n-1)!).

0, 2, 10, 48, 260, 1630, 11742, 95900, 876808, 8877690, 98641010, 1193556232, 15624736140, 220048367318, 3317652307270, 53319412081140, 909984632851472, 16436597430879730, 313262209859119578, 6282647653285676000, 132266266384961600020, 2916471173788403280462

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Also the number of positive integers with all distinct digits expressed in base n. E.g., a(10) = Sum_{j=1..10} A073531(j). - Labos Elemer, Dec 05 2002

For example, for n=3 we have 1, 2, 10, 12, 20, 21, 102, 120, 201, 210 (10 numbers in total). - Igor Krasikov, Aug 14 2023

Crossrefs

Cf. A001113, A073531, A073532.

a(n) = A001339(n)-1.

Equals (n-1)*A000522(n-1).

Programs

Mathematica

Table[Apply[Plus, Table[((b-1)/b)*Binomial[b, j]*j!, {j, 1, b}]], {b, 1, 25}]
Table[Floor[E(n-1)(n-1)!],{n,25}] (* Harvey P. Dale, May 19 2025 *)

Formula

G.f.: Q(0)/(2*x) - 1/x - 1/(1-x), where Q(k) = 1 + 1/(1 - x*(k+1)/(x*(k+1) + (1-x)/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 08 2013

a(n) = 2*(A038155(n) - A038155(n-1)). - Anton Zakharov, Oct 13 2016