A166677 - OEIS

%I #18 Jan 26 2023 10:10:40

%S 1,5,18,66,280,1420,8544,59836,478720,4308516,43085200,473937244,

%T 5687246976,73934210740,1035078950416,15526184256300,248418948100864,

%U 4223122117714756,76016198118865680,1444307764258447996

%N a(n)= n*(a(n-1)+4), a(0)=1.

%H G. C. Greubel, <a href="/A166677/b166677.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = n!+4*floor(e*n!)-4, n>0. [_Gary Detlefs_, Jun 06 2010]

%F From _Robert Israel_, May 22 2016: (Start)

%F a(n) = n!*(1 + Sum_{k=0..n-1} 4/k!) = n! + 4 e n Gamma(n,1).

%F E.g.f.: (1+4*x*exp(x))/(1-x). (End)

%p f:= gfun:-rectoproc({a(n)=n*(a(n-1)+4),a(0)=1},a(n),remember):

%p map(f, [$0..30]); # _Robert Israel_, May 22 2016

%t FoldList[#1*#2 + 4 #2 &, 1, Range[19]] (* _Robert G. Wilson v_, Jul 07 2012 *)

%Y Cf. A000142, A033540, A165792, A165813

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Oct 18 2009