A056543 a(n) = n*a(n-1) - 1 with a(1)=1.

1, 1, 2, 7, 34, 203, 1420, 11359, 102230, 1022299, 11245288, 134943455, 1754264914, 24559708795, 368395631924, 5894330110783, 100203611883310, 1803665013899579, 34269635264092000, 685392705281839999, 14393246810918639978, 316651429840210079515, 7282982886324831828844

Offset: 1

Author

Henry Bottomley, Jun 20 2000

Keywords

• easy
• nonn

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

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..450

Programs

Mathematica

nxt[{n_,a_}]:={n+1,a(n+1)-1}; NestList[nxt,{1,1},30][[All,2]] (* Harvey P. Dale, Dec 31 2022 *)

Formula

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

Extensions

More terms from James Sellers, Jul 04 2000