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a(n) = n*(a(n-1)+3), a(0)=1.
2

%I #16 Jan 23 2018 16:07:21

%S 1,4,14,51,216,1095,6588,46137,369120,3322107,33221100,365432133,

%T 4385185632,57007413255,798103785612,11971556784225,191544908547648,

%U 3256263445310067,58612742015581260,1113642098296043997

%N a(n) = n*(a(n-1)+3), a(0)=1.

%H G. C. Greubel, <a href="/A165813/b165813.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) = n! + 3*floor(e*n!) - 3. - _Gary Detlefs_, Jun 06 2010

%t FoldList[#1*#2 + 3 #2 &, 1, Range[19]] (* _Robert G. Wilson v_, Jul 07 2012 *)

%Y Cf. A000142, A033540, A165792.

%K nonn

%O 0,2

%A _Philippe Deléham_, Sep 28 2009