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%I #25 Sep 08 2022 08:46:05
%S 2,3,7,16,41,146,757,5090,40385,362962,3628901,39916922,479001745,
%T 6227020970,87178291397,1307674368226,20922789888257,355687428096290,
%U 6402373705728325,121645100408832362,2432902008176640401,51090942171709440442
%N n! + n^2 + 1.
%H Vincenzo Librandi, <a href="/A227546/b227546.txt">Table of n, a(n) for n = 0..200</a>
%F (n^3 -6*n^2 +11*n -7)*a(n) -(n^4 -5*n^3 +8*n^2 -5*n -1)*a(n-1) +(n-1)*(n^3 -3*n^2 +2*n -1)*a(n-2) = 0 for n>1. [_Bruno Berselli_, Jul 26 2013]
%t Table[n! + n^2 + 1, {n, 0, 30}].
%o (Magma) [Factorial(n)+n^2+1: n in [0..25]];
%o (Maxima) /* By the recurrence: */ a[0]:2$ a[1]:3$ a[n]:=(n^4-5*n^3+8*n^2-5*n-1)*a[n-1]/(n^3-6*n^2+11*n -7)-(n-1)*(n^3-3*n^2+2*n-1)*a[n-2]/(n^3-6*n^2+11*n-7)$ makelist(a[n], n, 0, 21); /* _Bruno Berselli_, Jul 26 2013 */
%Y Cf. A000142, A005095, A038507, A213169, A033312, A005096, A004664.
%Y Cf. A119662 (primes of the form n! + n^2 + 1).
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Jul 26 2013
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