A067273 a(n) = n*(a(n-1)*2+1), a(0) = 0.

0, 1, 6, 39, 316, 3165, 37986, 531811, 8508984, 153161721, 3063234430, 67391157471, 1617387779316, 42052082262229, 1177458303342426, 35323749100272795, 1130359971208729456, 38432239021096801521, 1383560604759484854774, 52575302980860424481431, 2103012119234416979257260, 88326509007845513128804941

Offset: 0

Author

Reinhard Zumkeller, Feb 21 2002

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..403

Crossrefs

Cf. A007526.

Programs

Maple

a := n -> n*hypergeom([1,1-n],[],-2):
seq(simplify(a(n)), n=0..17); # Peter Luschny, May 09 2017

Mathematica

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 *)

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

a(n) = Sum_{k=1..n} 2^(k-1)*k!*binomial(n,k). - Ridouane Oudra, Jun 15 2025

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Nov 15 2008