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

%I

%S 1,1,3,17,135,1349,16187,226617,3625871,65265677,1305313539,

%T 28716897857,689205548567,17919344262741,501741639356747,

%U 15052249180702409,481671973782477087,16376847108604220957

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

%C 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

%F a(n) = ceiling(2^n * n! * (2-sqrt(e))) = ceiling(A000165(n) * (2-sqrt(e))). - _Gary Detlefs_, Jul 18 2010

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

%t 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 *)

%K easy,nonn

%O 0,3

%A _Henry Bottomley_, Jun 19 2000

%E More terms from _James A. Sellers_, Jul 04 2000

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Last modified September 26 22:53 EDT 2020. Contains 337377 sequences. (Running on oeis4.)