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A191690 a(n) = n^n-n^(n-1)-n^(n-2)-...-n^2-n-1.

%I A191690 #26 Apr 22 2015 11:50:33
%S A191690 0,1,14,171,2344,37325,686286,14380471,338992928,8888888889,
%T A191690 256780503550,8105545862051,277635514376232,10257237069745861,
%U A191690 406615755353655134,17216961135462248175,775537745518440716416,37031913482632035365105
%N A191690 a(n) = n^n-n^(n-1)-n^(n-2)-...-n^2-n-1.
%H A191690 Danny Rorabaugh, <a href="/A191690/b191690.txt">Table of n, a(n) for n = 1..350</a>
%F A191690 a(n) = A117667(n)-1. - _Robert G. Wilson v_, Apr 16 2015
%F A191690 a(n) = n^n - A023037(n). - _Danny Rorabaugh_, Apr 20 2015
%e A191690 a(1)=0 (=1^1-1), a(2)=1 (=2^2-2-1), a(3)=14 (=3^3-3^2-3-1), a(4)=171 (=4^4-4^3-4^2-4-1).
%p A191690 A191690 := proc(n) n^n-add( n^j,j=0..n-1) ; end proc: # _R. J. Mathar_, Jun 23 2011
%t A191690 Table[Total[-n^Range[0,n-1]]+n^n,{n,2,20}] (* _Harvey P. Dale_, Jul 06 2011 *)
%t A191690 f[n_] := ((n - 2) n^n + n)/(n - 1) - 1; f[1] = 0; Array[f, 18] (* _Robert G. Wilson v_, Apr 16 2015 *)
%o A191690 (PARI) a(n) = n^n - sum(k=0, n-1, n^k); \\ _Michel Marcus_, Apr 16 2015
%o A191690 (Sage) [n^n - sum([n^k for k in range(n)]) for n in range(1,19)] # _Danny Rorabaugh_, Apr 20 2015
%Y A191690 Cf. A000312, A023037, A191686.
%K A191690 nonn
%O A191690 1,3
%A A191690 _Juri-Stepan Gerasimov_, Jun 11 2011