A004664 a(n) = n! + n^2.

1, 2, 6, 15, 40, 145, 756, 5089, 40384, 362961, 3628900, 39916921, 479001744, 6227020969, 87178291396, 1307674368225, 20922789888256, 355687428096289, 6402373705728324, 121645100408832361, 2432902008176640400, 51090942171709440441, 1124000727777607680484

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

It appears that n! + n^2 is not a perfect square for n >= 1. - Alexander R. Povolotsky, Sep 26 2008

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for sequences related to factorial numbers

Programs

Magma

[Factorial(n) + n^2: n in [0..25]]; // Vincenzo Librandi, Jul 26 2013

Mathematica

Table[n! + n^2, {n, 0, 20}] (* Stefan Steinerberger, Apr 11 2006 *)

Formula

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

Extensions

One more term from Stefan Steinerberger, Apr 11 2006