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Search: id:A001564
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| A001564 |
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2nd differences of factorial numbers.
(Formerly M2972 N1202)
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+0
13
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| 1, 3, 14, 78, 504, 3720, 30960, 287280, 2943360, 33022080, 402796800, 5308934400, 75203251200, 1139544806400, 18394619443200, 315149522688000, 5711921639424000, 109196040425472000, 2196014181064704000, 46346783255764992000, 1024251745442365440000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is also the number of isolated fixed points (i.e. adjacent entries are not fixed points) in all permutations of [n+2]. Example: a(2)=14 because we have (the isolated fixed points are marked) 1'423, 1'324', 1'342, 1'43'2, 413'2, 3124', 42'13, 2314', 243'1, 32'14', 32'41. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 18 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
A. van Heemert, Cyclic permutations with sequences and related problems, J. Reine Angew. Math., 198 (1957), 56-72.
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for sequences related to factorial numbers
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FORMULA
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a(n) = (n^2 + n + 1)*n! = A002061(n-1)*A000142(n) - Mitch Harris (maharri(AT)gmail.com), Jul 10 2008
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MAPLE
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seq(factorial(n)*(n^2+n+1), n = 0 .. 20); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 18 2009]
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CROSSREFS
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Cf. A047920.
Sequence in context: A048779 A052186 A074538 this_sequence A059276 A003169 A086621
Adjacent sequences: A001561 A001562 A001563 this_sequence A001565 A001566 A001567
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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