|
%I #27 Sep 08 2022 08:45:15
%S 1,2,6,26,158,1266,12662,151946,2127246,34035938,612646886,
%T 12252937722,269564629886,6469551117266,168208329048918,
%U 4709833213369706,141294996401091182,4521439884834917826,153728956084387206086
%N a(n+1) = 2*n*a(n) + 2 with a(0)=1.
%C Row sums of triangle A099759.
%C 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
%H G. C. Greubel, <a href="/A099760/b099760.txt">Table of n, a(n) for n = 0..400</a>
%F a(n) = 2^n*(n-1)! + 2*floor(2^(n-1)*(n-1)!*(exp(1/2)-1)), n>0. - _Gary Detlefs_, Jul 14 2010
%F a(n+1) = 2^(n+1)*(n!)*(Sum_{k=0..n} 1/(2^k*(k!))) for n>=0. - _Werner Schulte_, Apr 22 2017
%e a(3)=26, so a(4)=2*3*26+2=158.
%p 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
%t RecurrenceTable[{a[0]==1,a[n]==2(n-1)a[n-1]+2},a,{n,20}] (* _Harvey P. Dale_, Jan 31 2014 *)
%o (PARI) a(n) = if(n==0, 1, 2*(n-1)*a(n-1) + 2);
%o vector(20, n, a(n-1)) \\ _G. C. Greubel_, Sep 03 2019
%o (Magma) a:= func< n | n eq 0 select 1 else 2*(n-1)*Self(n-1) + 2 >;
%o [a(n): n in [0..20]]; // _G. C. Greubel_, Sep 03 2019
%o (Sage)
%o def a(n):
%o if (n==0): return 1
%o else: return 2*(n-1)*a(n-1) + 2
%o [a(n) for n in (0..20)] # _G. C. Greubel_, Sep 03 2019
%o (GAP)
%o a:= function(n)
%o if n=0 then return 1;
%o else return 2*(n-1)*a(n-1) + 2;
%o fi;
%o end;
%o List([0..20], n-> a(n) ); # _G. C. Greubel_, Sep 03 2019
%K easy,nonn
%O 0,2
%A _Miklos Kristof_, Nov 11 2004
%E More terms from _Emeric Deutsch_, Feb 23 2005
%E Edited by _Philippe Deléham_, Feb 17 2007
| 