A117643 a(n) = n*(a(n-1)-1) starting with a(0)=3.

3, 2, 2, 3, 8, 35, 204, 1421, 11360, 102231, 1022300, 11245289, 134943456, 1754264915, 24559708796, 368395631925, 5894330110784, 100203611883311, 1803665013899580, 34269635264092001, 685392705281840000

Offset: 0

Author

Henry Bottomley, Apr 10 2006

Keywords

• easy
• nonn

Comments

Starting with a(0)=0 would give -A007526(n); starting with a(0)=1 would give -A038156(n). In general, for this recurrence, a(n) = ceiling(1 + n!*(a(0)-e)) for n>0; this is the first case with positive terms.

Examples

			a(5) = 5*(a(4)-1) = 5*(8-1) = 35.
		

Programs

Mathematica

a=3;Table[a=a*n-n,{n,1,2*4!}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2010 *)
RecurrenceTable[{a[0]==3,a[n]==n(a[n-1]-1)},a,{n,20}] (* Harvey P. Dale, Jul 17 2018 *)

Formula

a(n) = ceiling(1 + n!*(3-e)) for n>0.

a(n) = n! - floor(e*n!) + 1, n>0. - Gary Detlefs, Jun 06 2010