A166677 a(n)= n*(a(n-1)+4), a(0)=1.
1, 5, 18, 66, 280, 1420, 8544, 59836, 478720, 4308516, 43085200, 473937244, 5687246976, 73934210740, 1035078950416, 15526184256300, 248418948100864, 4223122117714756, 76016198118865680, 1444307764258447996
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..200
Programs
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Maple
f:= gfun:-rectoproc({a(n)=n*(a(n-1)+4),a(0)=1},a(n),remember): map(f, [$0..30]); # Robert Israel, May 22 2016 -
Mathematica
FoldList[#1*#2 + 4 #2 &, 1, Range[19]] (* Robert G. Wilson v, Jul 07 2012 *)
Formula
a(n) = n!+4*floor(e*n!)-4, n>0. [Gary Detlefs, Jun 06 2010]
From Robert Israel, May 22 2016: (Start)
a(n) = n!*(1 + Sum_{k=0..n-1} 4/k!) = n! + 4 e n Gamma(n,1).
E.g.f.: (1+4*x*exp(x))/(1-x). (End)