A099760 a(n+1) = 2*n*a(n) + 2 with a(0)=1.

1, 2, 6, 26, 158, 1266, 12662, 151946, 2127246, 34035938, 612646886, 12252937722, 269564629886, 6469551117266, 168208329048918, 4709833213369706, 141294996401091182, 4521439884834917826, 153728956084387206086

Offset

0,2

Comments

Row sums of triangle A099759.

For n > 1, a(n) equals 2^n times the permanent of the (n-1) X (n-1) matrix with (3/2)'s along the main diagonal and 1's everywhere else. - John M. Campbell, Jun 03 2011

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

Formula

a(n) = 2^n*(n-1)! + 2*floor(2^(n-1)*(n-1)!*(exp(1/2)-1)), n>0. - Gary Detlefs, Jul 14 2010

a(n+1) = 2^(n+1)*(n!)*(Sum_{k=0..n} 1/(2^k*(k!))) for n>=0. - Werner Schulte, Apr 22 2017

Example

a(3)=26, so a(4)=2*3*26+2=158.

Maple

a[0]:=1: for n from 0 to 21 do a[n+1]:=2*n*a[n]+2 od: seq(a[n], n=0..21); # Emeric Deutsch, Feb 23 2005

Mathematica

RecurrenceTable[{a[0]==1, a[n]==2(n-1)a[n-1]+2}, a, {n, 20}] (* Harvey P. Dale, Jan 31 2014 *)

Prog

(PARI) a(n) = if(n==0, 1, 2*(n-1)*a(n-1) + 2);
vector(20, n, a(n-1)) \\ G. C. Greubel, Sep 03 2019
(Magma) a:= func< n | n eq 0 select 1 else 2*(n-1)*Self(n-1) + 2 >;
[a(n): n in [0..20]]; // G. C. Greubel, Sep 03 2019
(Sage)
def a(n):
    if (n==0): return 1
    else: return 2*(n-1)*a(n-1) + 2
[a(n) for n in (0..20)] # G. C. Greubel, Sep 03 2019
(GAP)
a:= function(n)
    if n=0 then return 1;
    else return 2*(n-1)*a(n-1) + 2;
    fi;
  end;
List([0..20], n-> a(n) ); # G. C. Greubel, Sep 03 2019

Crossrefs

Sequence in context: A123306 A218691 A099758 * A112934 A135922 A213430

Adjacent sequences: A099757 A099758 A099759 * A099761 A099762 A099763

Keyword

easy,nonn

Author

Miklos Kristof, Nov 11 2004

Extensions

More terms from Emeric Deutsch, Feb 23 2005

Edited by Philippe Deléham, Feb 17 2007

Status

approved