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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

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

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

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Last modified June 18 20:45 EDT 2021. Contains 345121 sequences. (Running on oeis4.)