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0, 0, 2, 21, 232, 3005, 45936, 818503, 16736896, 387057609, 9996371200, 285271753811, 8915621446656, 302868879571453, 11111919647266816, 437892582706491375, 18446723150919663616, 827239906198908668177, 39346401672922831847424
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n)=|non-injective functions [n]->[n]|=|non-surjective functions [n]->[n]|
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 (FrankTAW(AT)Netscape.net), Dec 28 2006
n^n > n! for n >= 3. [Mitrinovic]
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REFERENCES
| D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 193, 3.1.22.
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LINKS
| T. D. Noe and Vincenzo Librandi, Table of n, a(n) for n = 0..300 [T. D. Noe computed terms 0-50, May 11 2007;Vincenzo Librandi computed the first 300 terms, Aug 22 2011]
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MATHEMATICA
| lst={}; Do[AppendTo[lst, n^n-n! ], {n, 3*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 20 2008]
Join[{0}, Table[n^n-n!, {n, 20}]] (* From Harvey P. Dale, Oct 11 2011 *)
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PROG
| (MAGMA) [(n^n-Factorial(n)): n in [0..20] ]; // Vincenzo Librandi, Aug 22 2011
(PARI) a(n)=n^n-n! \\ Charles R Greathouse IV, Aug 22 2011
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CROSSREFS
| Cf. A126130.
Sequence in context: A062813 A024231 A069717 * A134490 A045726 A105712
Adjacent sequences: A036676 A036677 A036678 * A036680 A036681 A036682
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), G. L. Honaker, Jr. (honak3r(AT)gmail.com)
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