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A117643 a(n) = n*(a(n-1)-1) starting with a(0)=3. 0
3, 2, 2, 3, 8, 35, 204, 1421, 11360, 102231, 1022300, 11245289, 134943456, 1754264915, 24559708796, 368395631925, 5894330110784, 100203611883311, 1803665013899580, 34269635264092001, 685392705281840000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

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

a(n) = 3*n! - n! * sum_{k=0..n} 1/(k-1)!, with n>=0. - Paolo P. Lava, Oct 07 2008

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

EXAMPLE

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

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 *)

CROSSREFS

Sequence in context: A032450 A046460 A327661 * A141862 A237612 A111739

Adjacent sequences:  A117640 A117641 A117642 * A117644 A117645 A117646

KEYWORD

easy,nonn

AUTHOR

Henry Bottomley, Apr 10 2006

STATUS

approved

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Last modified May 15 07:51 EDT 2021. Contains 343909 sequences. (Running on oeis4.)