A055214 a(0) = 1; a(n) = 2*n*a(n-1) - 1 for n >= 1.

1, 1, 3, 17, 135, 1349, 16187, 226617, 3625871, 65265677, 1305313539, 28716897857, 689205548567, 17919344262741, 501741639356747, 15052249180702409, 481671973782477087, 16376847108604220957

Offset

0,3

Comments

a(n) is a specific instance of sequences having the form a(0)= x, a(n) = a*n*a(n-1)+k. (Here x =1, a = 2, and k =- 1). Sequences of this form have a closed form of n!*a^n*x + k*sum(n!*a^(n-j)/j!, j = 1..n). -Gary Detlefs, Mar 26 2018

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = ceiling(2^n * n! * (2-sqrt(e))) = ceiling(A000165(n) * (2-sqrt(e))). - Gary Detlefs, Jul 18 2010

Example

a(3) = 2*3*a(2) - 1 = 6*3 - 1 = 17.

Mathematica

s=-1; lst={Abs[s]}; Do[s+=s++n; AppendTo[lst, Abs[s]], {n, 1, 5!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 23 2008 *)

Crossrefs

Sequence in context: A093986 A192459 A362748 * A105630 A199138 A006290

Adjacent sequences: A055211 A055212 A055213 * A055215 A055216 A055217

Keyword

easy,nonn

Author

Henry Bottomley, Jun 19 2000

Extensions

More terms from James A. Sellers, Jul 04 2000

Status

approved