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A225658 a(n) = n! + (n+1)! + 3*(n+2)!.

%I A225658 #26 Sep 08 2022 08:46:05
%S A225658 8,21,80,390,2304,15960,126720,1134000,11289600,123742080,1480550400,
%T A225658 19199980800,268240896000,4016428416000,64163222323200,
%U A225658 1089292748544000,19583731335168000,371693362360320000,7426753498644480000,155827373623713792000
%N A225658 a(n) = n! + (n+1)! + 3*(n+2)!.
%C A225658 In factorial base representation (A007623) the terms are written as: 110, 311, 3110, 31100, 311000, ... From a(1) = 21 = "311" onwards each term always begins with "311", followed by n-1 zeros. - _Antti Karttunen_, Sep 24 2016
%H A225658 Vincenzo Librandi, <a href="/A225658/b225658.txt">Table of n, a(n) for n = 0..200</a>
%H A225658 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A225658 a(n) = A211369(3,n).
%F A225658 3*a(n) -(3*n+5)*a(n-1) +(1-n)*a(n-2) +(2-n)*a(n-3) = 0.
%F A225658 E.g.f: (3*x-x^2-8)/(x-1)^3. - _Benedict W. J. Irwin_, Sep 27 2016
%p A225658 A225658 := proc(n)
%p A225658     n!+(n+1)!+3*(n+2)! ;
%p A225658 end proc:
%t A225658 #[[1]]+#[[2]]+3#[[3]]&/@Partition[Range[0,30]!,3,1] (* _Harvey P. Dale_, Apr 08 2014 *)
%t A225658 Table[CoefficientList[Series[(3x-x^2-8)/(x-1)^3,{x,0,30}], x][[n]](n-1)!,{n,1,30}] (* _Benedict W. J. Irwin_, Sep 27 2016 *)
%o A225658 (Magma) [Factorial(n) +Factorial(n+1)+3*Factorial(n+2): n in [0..20]]; // _Vincenzo Librandi_, Apr 09 2014
%o A225658 (Scheme) (define (A225658 n) (+ (A000142 n) (A000142 (+ 1 n)) (* 3 (A000142 (+ 2 n))))) ;; _Antti Karttunen_, Sep 24 2016
%Y A225658 Cf. A000142.
%Y A225658 Row 3 of A211369, row 16 of A276955 (from a(1)=21 onward).
%K A225658 easy,nonn
%O A225658 0,1
%A A225658 _R. J. Mathar_, May 11 2013