Search: id:A001564
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%I A001564 M2972 N1202
%S A001564 1,3,14,78,504,3720,30960,287280,2943360,33022080,402796800,5308934400,
%T A001564 75203251200,1139544806400,18394619443200,315149522688000,5711921639424000,
%U A001564 109196040425472000,2196014181064704000,46346783255764992000,1024251745442365440000
%N A001564 2nd differences of factorial numbers.
%C A001564 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]
%D A001564 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001564 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001564 A. van Heemert, Cyclic permutations with sequences and related problems, 
               J. Reine Angew. Math., 198 (1957), 56-72.
%H A001564 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas 
               for Some Functions on Finite Sets</a>
%H A001564 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>
%F A001564 a(n) = (n^2 + n + 1)*n! = A002061(n-1)*A000142(n) - Mitch Harris (maharri(AT)gmail.com), 
               Jul 10 2008
%p A001564 seq(factorial(n)*(n^2+n+1), n = 0 .. 20); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 18 2009]
%Y A001564 Cf. A047920.
%Y A001564 Sequence in context: A048779 A052186 A074538 this_sequence A059276 A003169 
               A086621
%Y A001564 Adjacent sequences: A001561 A001562 A001563 this_sequence A001565 A001566 
               A001567
%K A001564 nonn,easy
%O A001564 0,2
%A A001564 N. J. A. Sloane (njas(AT)research.att.com).

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