The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005442 a(n) = n!*Fibonacci(n+1). (Formerly M3549) 21
 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 Another way to state the first comment: a(n) is the number of ways to partition [n] into blocks of size at most 2, order the blocks, and order the elements within each block. For example, a(5)=960 since there are 3 cases: 1) 1,2,3,4,5: 120 such ordered blocks, 1 way to order elements within blocks, hence 120 ways; 2) 12,3,4,5: 240 such ordered blocks, 2 ways to order elements within blocks, hence 480 ways; 3) 12,34,5: 90 such ordered blocks, 4 ways to order elements within blocks, hence 360 ways. - Enrique Navarrete, Sep 01 2023 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..416 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/0606404 [math.CO], 2006-2007. Index entries for related partition-counting sequences FORMULA a(n) = A039948(n,0). E.g.f.: 1/(1-x-x^2). D-finite with recurrence 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 (Magma) [Factorial(n)*Fibonacci(n+1): n in [0..20]]; // G. C. Greubel, Nov 20 2022 (SageMath) [fibonacci(n+1)*factorial(n) for n in range(21)] # G. C. Greubel, Nov 20 2022 CROSSREFS Row sums of Fibonacci Jabotinsky-triangle A039692. Cf. A000045, A000142, A039948, A052585, A080599. Sequence in context: A296982 A222375 A053529 * A306881 A367489 A084661 Adjacent sequences: A005439 A005440 A005441 * A005443 A005444 A005445 KEYWORD nonn,easy AUTHOR Simon Plouffe EXTENSIONS Comments from Wolfdieter Lang STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 04:02 EDT 2024. Contains 372900 sequences. (Running on oeis4.)