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A108217
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a(0) = 1, a(1) = 1, a(n) = n! + (n-2)! for n >= 2.
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4
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1, 1, 3, 7, 26, 126, 744, 5160, 41040, 367920, 3669120, 40279680, 482630400, 6266937600, 87657292800, 1313901388800, 21009968179200, 356995102464000, 6423296495616000, 122000787836928000, 2439304381882368000, 51212587272118272000, 1126433629785784320000
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..22.
Index entries for sequences related to factorial base representation
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FORMULA
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For n >= 2, a(n) = A002061(n) * (n-2)! - Antti Karttunen, Sep 23 2016
E.g.f.: x + (1-x)*log(1-x) + 1/(1-x). - Andrew Howroyd, May 09 2021
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EXAMPLE
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a(6) = 6!+4! = 720+24 = 744.
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MAPLE
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a:= n-> `if`(n<2, 1, n!+(n-2)!):
seq(a(n), n=0..30);
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MATHEMATICA
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Table[If[n<2, 1, n!+(n-2)!], {n, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
Join[{1, 1}, #[[1]]+#[[3]]&/@Partition[Range[0, 20]!, 3, 1]] (* Harvey P. Dale, Nov 19 2015 *)
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PROG
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(Scheme) (define (A108217 n) (if (<= n 1) 1 (* (A002061 n) (A000142 (- n 2))))) ;; Antti Karttunen, Sep 23 2016
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CROSSREFS
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Cf. A000142, A002061, A007623, A001048, A030495.
Row 5 of A276955, from term a(3)=7 onward.
Sequence in context: A057005 A158561 A252786 * A120120 A126472 A019059
Adjacent sequences: A108214 A108215 A108216 * A108218 A108219 A108220
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KEYWORD
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easy,nonn
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AUTHOR
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Miklos Kristof, following a suggestion from Peter Boros, (borospet(AT)freemail.hu), Jun 16 2005
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EXTENSIONS
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Corrected by Georg Fischer, May 09 2021
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STATUS
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approved
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