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A067273
a(n) = n*(a(n-1)*2+1), a(0) = 0.
3
0, 1, 6, 39, 316, 3165, 37986, 531811, 8508984, 153161721, 3063234430, 67391157471, 1617387779316, 42052082262229, 1177458303342426, 35323749100272795, 1130359971208729456, 38432239021096801521
OFFSET
0,3
LINKS
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
Cf. A007526.
Sequence in context: A289996 A335344 A135890 * A187117 A137972 A007322
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 21 2002
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Nov 15 2008
STATUS
approved