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%I #26 May 09 2021 17:34:47
%S 1,1,3,7,26,126,744,5160,41040,367920,3669120,40279680,482630400,
%T 6266937600,87657292800,1313901388800,21009968179200,356995102464000,
%U 6423296495616000,122000787836928000,2439304381882368000,51212587272118272000,1126433629785784320000
%N a(0) = 1, a(1) = 1, a(n) = n! + (n-2)! for n >= 2.
%C In factorial base representation (A007623) the terms of this sequence look as: 1, 1, 11, 101, 1010, 10100, 101000, ... From a(3)=7 onward each term begins always with "101", which is then followed by n-3 zeros. - _Antti Karttunen_, Sep 23 2016
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F For n >= 2, a(n) = A002061(n) * (n-2)! - _Antti Karttunen_, Sep 23 2016
%F E.g.f.: x + (1-x)*log(1-x) + 1/(1-x). - _Andrew Howroyd_, May 09 2021
%e a(6) = 6!+4! = 720+24 = 744.
%p a:= n-> `if`(n<2, 1, n!+(n-2)!):
%p seq(a(n), n=0..30);
%t Table[If[n<2,1,n!+(n-2)!],{n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, May 19 2011 *)
%t Join[{1,1},#[[1]]+#[[3]]&/@Partition[Range[0,20]!,3,1]] (* _Harvey P. Dale_, Nov 19 2015 *)
%o (Scheme) (define (A108217 n) (if (<= n 1) 1 (* (A002061 n) (A000142 (- n 2))))) ;; _Antti Karttunen_, Sep 23 2016
%Y Cf. A000142, A002061, A007623, A001048, A030495.
%Y Row 5 of A276955, from term a(3)=7 onward.
%K easy,nonn
%O 0,3
%A _Miklos Kristof_, following a suggestion from Peter Boros, (borospet(AT)freemail.hu), Jun 16 2005
%E Corrected by _Georg Fischer_, May 09 2021
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