A227546 n! + n^2 + 1.

2, 3, 7, 16, 41, 146, 757, 5090, 40385, 362962, 3628901, 39916922, 479001745, 6227020970, 87178291397, 1307674368226, 20922789888257, 355687428096290, 6402373705728325, 121645100408832362, 2432902008176640401, 51090942171709440442

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

(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]

Mathematica

Table[n! + n^2 + 1, {n, 0, 30}].

Prog

(Magma) [Factorial(n)+n^2+1: n in [0..25]];
(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 */

Crossrefs

Cf. A000142, A005095, A038507, A213169, A033312, A005096, A004664.

Cf. A119662 (primes of the form n! + n^2 + 1).

Sequence in context: A247332 A162092 A143884 * A301902 A332885 A122031

Adjacent sequences: A227543 A227544 A227545 * A227547 A227548 A227549

Keyword

nonn,easy

Author

Vincenzo Librandi, Jul 26 2013

Status

approved