A117667 a(n) = n^n - n^(n-1) - n^(n-2) - n^(n-3) - ... - n^3 - n^2 - n.

1, 1, 2, 15, 172, 2345, 37326, 686287, 14380472, 338992929, 8888888890, 256780503551, 8105545862052, 277635514376233, 10257237069745862, 406615755353655135, 17216961135462248176, 775537745518440716417, 37031913482632035365106, 1868507452568073945283759

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..386 (terms n = 1..100 from Christian N. K. Anderson)

Formula

a(n) = A000312(n) - A023037(n) + 1 for n>=1. - Michel Marcus, Apr 14 2015

a(n) = A191690(n) + 1 for n>=1. - Robert G. Wilson v, Apr 16 2015

Example

a(3) = 3^3-3^2-3 = 27-9-3 = 15.

Maple

a:=n->n^n-sum(n^j, j=1..n-1): seq(a(n), n=0..19); # Emeric Deutsch, Apr 16 2006

Mathematica

s[n_] := Sum[n^i, {i, 1, n - 1}]; Table[n^n - s[n], {n, 17}] (* Carlos Eduardo Olivieri, Apr 14 2015 *)
(* Alternative: *)
f[n_] := ((n - 2) n^n + n)/(n - 1); f[1] = 1; Array[f, 18] (* Robert G. Wilson v, Apr 15 2015 *)

Prog

(PARI) a(n)= if(n<2, 1, (n^n*(n-2)+n)/(n-1)); \\ Ruud H.G. van Tol, Apr 28 2026

Crossrefs

Cf. A000312 (n^n), A023037 (1+n+n^2+...n^(n-1)), A001923, A031972, A191690, A341331 (n^n-(n-1)^n-...).

Sequence in context: A262035 A264793 A228840 * A360483 A222920 A036080

Adjacent sequences: A117664 A117665 A117666 * A117668 A117669 A117670

Keyword

nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 11 2006

Extensions

a(0)=1 prepended by Alois P. Heinz, Apr 28 2026

Status

approved