login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..18.

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

Index entries for related partition-counting sequences

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

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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