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 A005442 a(n) = n!*Fibonacci(n+1). (Formerly M3549) 18
 1, 1, 4, 18, 120, 960, 9360, 105840, 1370880, 19958400, 322963200, 5748019200, 111607372800, 2347586841600, 53178757632000, 1290674601216000, 33413695451136000, 919096314200064000, 26768324463648768000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of ways to use the elements of {1,...,n} once each to form a sequence of lists, each having length 1 or 2. - Bob Proctor, Apr 18 2005 Number of pairs (p,S) where p is a permutation of {1,2,...,n} and S is a subset of {1,2,...,n} such that if s is in S then p(s) is not in S.  For example a(2) = 4 because we have (p=(1)(2), s={}); (p=(1,2), s={}); (p=(1,2), s={1}); (p=(1,2), s={2}) where p is given in cycle notation. - Geoffrey Critzer, Jul 01 2013 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS P. R. J. Asveld & N. J. A. Sloane, Correspondence, 1987 P. R. J. Asveld, A family of Fibonacci-like sequences, Fib. Quart., 25 (1987), 81-83. P. R. J. Asveld, Another family of Fibonacci-like sequences, Fib. Quart., 25 (1987), 361-364. P. R. J. Asveld, Fibonacci-like differential equations with a polynomial nonhomogeneous term, Fib. Quart. 27 (1989), 303-309. INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 494 Robert A. Proctor, Let's Expand Rota's Twelvefold Way For Counting Partitions!, arXiv:math.CO/0606404, Jan 05, 2007 FORMULA a(n) = A039948(n,0). E.g.f.: 1/(1-x-x^2). a(n) = n*a(n-1)+n*(n-1)*a(n-2). - Detlef Pauly (dettodet(AT)yahoo.de), Sep 22 2003 a(n) = D^n(1/(1-x)) evaluated at x = 0, where D is the operator sqrt(1+4*x)*d/dx. Cf. A080599 and A052585. - Peter Bala, Dec 07 2011 MATHEMATICA Table[Fibonacci[n + 1]*n!, {n, 0, 20}] - Zerinvary Lajos, Jul 09 2009 PROG (PARI) a(n) = n!*fibonacci(n+1) \\ Charles R Greathouse IV, Oct 03 2016 CROSSREFS Row sums of Fibonacci Jabotinsky-triangle A039692. A080599 and A052585. Sequence in context: A296982 A222375 A053529 * A306881 A084661 A112294 Adjacent sequences:  A005439 A005440 A005441 * A005443 A005444 A005445 KEYWORD nonn,easy AUTHOR EXTENSIONS Comments from Wolfdieter Lang STATUS approved

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Last modified July 17 02:10 EDT 2019. Contains 325092 sequences. (Running on oeis4.)