A089043 a(n) = n!^2 + (-1)^n.

0, 5, 35, 577, 14399, 518401, 25401599, 1625702401, 131681894399, 13168189440001, 1593350922239999, 229442532802560001, 38775788043632639999, 7600054456551997440001, 1710012252724199423999999, 437763136697395052544000001, 126513546505547170185215999999

Offset: 1

Author

Serge Boisse (serge.boisse(AT)aviation-civile.gouv.fr), Dec 02 2003

Keywords

• easy
• nonn

Comments

p = 2*n+1 is prime iff it divides a(n) (Wilson's theorem) for instance let n=5, p =11 : a(5) = 14399 = 11*1309, so 11 is prime.

Examples

			a(5) = 14399 because 14399=(5!)^2+(-1)^5.
		

Programs

PARI

a(n) = n!^2+(-1)^n; \\ Michel Marcus, Oct 02 2016

Formula

a(n) = n^2*(a(n-1)-(-1)^(n-1))+(-1)^n.

Extensions

Offset corrected and edited by Michel Marcus, Oct 02 2016