OFFSET
0,3
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..403
FORMULA
E.g.f.: x*exp(x)/(1-2*x). a(n) = n!*Sum_{k=1..n} 2^(k-1)/(n-k)! = n*A010844(n-1). - Vladeta Jovovic, Feb 09 2003
a(n) ~ n! * exp(1/2) * 2^(n-1). - Vaclav Kotesovec, Oct 05 2013
a(n) = n*hypergeom([1,1-n], [], -2). - Peter Luschny, May 09 2017
MAPLE
a := n -> n*hypergeom([1, 1-n], [], -2):
seq(simplify(a(n)), n=0..17); # Peter Luschny, May 09 2017
MATHEMATICA
s=1; lst={}; Do[s+=(s*=n)-n; AppendTo[lst, Abs[s]], {n, 0, 5!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)
FoldList[2 #1*#2 + #2 &, 0, Range[19]] (* Robert G. Wilson v, Jul 07 2012 *)
a[n_] := 2^(n-1)*Sqrt[E]*n*Gamma[n, 1/2];
Table[a[n] // FullSimplify, {n, 0, 20}] (* Gerry Martens, Jun 28 2015 *)
nxt[{n_, a_}]:={n+1, (n+1)(2*a+1)}; NestList[nxt, {0, 0}, 20][[;; , 2]] (* Harvey P. Dale, Jun 26 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 21 2002
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Nov 15 2008
STATUS
approved