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A036679 a(n) = n^n - n!. 11

%I

%S 0,0,2,21,232,3005,45936,818503,16736896,387057609,9996371200,

%T 285271753811,8915621446656,302868879571453,11111919647266816,

%U 437892582706491375,18446723150919663616,827239906198908668177,39346401672922831847424

%N a(n) = n^n - n!.

%C a(n) = |non-injective functions [n]->[n]| = |non-surjective functions [n]->[n]|.

%C Fit a polynomial f of degree n-1 to the first n n-th powers of nonnegative integers. Then a(n) = f(n). - _Franklin T. Adams-Watters_, Dec 28 2006

%C n^n > n! for n >= 3. [Mitrinovic]

%D D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 193, 3.1.22.

%H T. D. Noe and Vincenzo Librandi, <a href="/A036679/b036679.txt">Table of n, a(n) for n = 0..300</a> [T. D. Noe computed terms 0-50, May 11 2007; Vincenzo Librandi computed the first 300 terms, Aug 22 2011]

%F E.g.f.: 1/(1-T(x))-1/(1-x) where T(x) is the e.g.f. for A000169. - _Geoffrey Critzer_, Dec 10 2012

%t Join[{0}, Table[n^n - n!, {n, 20}]] (* _Harvey P. Dale_, Oct 11 2011 *)

%o (MAGMA) [(n^n-Factorial(n)): n in [0..20] ]; // _Vincenzo Librandi_, Aug 22 2011

%o (PARI) a(n)=n^n-n! \\ _Charles R Greathouse IV_, Aug 22 2011

%Y Cf. A126130, diagonal of A101030.

%K nonn,easy,nice

%O 0,3

%A _N. J. A. Sloane_, _G. L. Honaker, Jr._

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Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)