|
%I #29 Feb 09 2023 12:42:44
%S 1,2,6,15,40,145,756,5089,40384,362961,3628900,39916921,479001744,
%T 6227020969,87178291396,1307674368225,20922789888256,355687428096289,
%U 6402373705728324,121645100408832361,2432902008176640400,51090942171709440441,1124000727777607680484
%N a(n) = n! + n^2.
%C It appears that n! + n^2 is not a perfect square for n >= 1. - _Alexander R. Povolotsky_, Sep 26 2008
%H Vincenzo Librandi, <a href="/A004664/b004664.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F Possible recurrence relation (according to WolframAlpha): a(n+2) = ((n+2)*(n^3+n^2-n-2)*a(n+1))/(n^3-2*n-1)-((n+2)*(n^2+n-1)*a(n))/(n^2-n-1). - _Alexander R. Povolotsky_, Nov 06 2010
%t Table[n! + n^2, {n, 0, 20}] (* _Stefan Steinerberger_, Apr 11 2006 *)
%o (Magma) [Factorial(n) + n^2: n in [0..25]]; // _Vincenzo Librandi_, Jul 26 2013
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E One more term from _Stefan Steinerberger_, Apr 11 2006
|
