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A056543 a(n) = n*a(n-1) - 1 with a(1)=1. 2
1, 1, 2, 7, 34, 203, 1420, 11359, 102230, 1022299, 11245288, 134943455, 1754264914, 24559708795, 368395631924, 5894330110783, 100203611883310, 1803665013899579, 34269635264092000, 685392705281839999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

If s(n) is a sequence defined by s(0)=x, s(n)=(n+1)*s(n-1)+k, n>0, then s(n) = n!*x +(n! - a(n+1))*k. - Gary Detlefs, Jun 10 2010

LINKS

Table of n, a(n) for n=1..20.

FORMULA

a(n) = ceiling((3-e)*n!) = n! - A056542(n) = 2*n! - A002627(n) = 3*n! - A000522(n).

a(n) = n!*(2-Sum_{k=1..n}{k!^(-1)}), with n>=1. - Paolo P. Lava, Jun 25 2010

EXAMPLE

a(4) = 4*a(3) - 1 = 4*2 - 1 = 7.

MATHEMATICA

lst={1}; s=-1; Do[s+=s++n; AppendTo[lst, Abs[s]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 23 2008 *)

CROSSREFS

Sequence in context: A117399 A145345 A212027 * A075834 A011800 A112916

Adjacent sequences:  A056540 A056541 A056542 * A056544 A056545 A056546

KEYWORD

easy,nonn

AUTHOR

Henry Bottomley, Jun 20 2000

EXTENSIONS

More terms from James A. Sellers, Jul 04 2000

STATUS

approved

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Last modified April 19 06:59 EDT 2015. Contains 256803 sequences.