OFFSET
0,3
COMMENTS
From Enrique Navarrete, Aug 28 2025: (Start)
Number of ways to seat n people on linearly ordered benches placing an odd number of people on each bench.
For example, a(7) = 65520 since the number of ways are (number of people in parentheses):
1 bench (7): 5040 ways;
3 benches (5,1,1): 15120 ways;
3 benches (3,3,1): 15120 ways;
5 benches (3,1,1,1,1): 25200 ways;
7 benches (1,1,1,1,1,1,1): 5040 ways.
If the benches are not linearly ordered the number of ways is A088009. (End)
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, Fibonacci-like differential equations with a polynomial nonhomogeneous term, Fib. Quart. 27 (1989), 303-309.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 511
FORMULA
a(n) = A039948(n, 1).
E.g.f.: x/(1-x-x^2). - Geoffrey Critzer, Sep 01 2013
a(n) = n*a(n-1) + n*(n-1)*a(n-2). - G. C. Greubel, Nov 20 2022
MAPLE
ZL:=[S, {a = Atom, b = Atom, S = Prod(X, Sequence(Prod(X, b))), X = Sequence(b, card >= 1)}, labelled]: seq(combstruct[count](ZL, size=n), n=0..18); # Zerinvary Lajos, Mar 26 2008
MATHEMATICA
Table[Fibonacci[n]*n!, {n, 0, 25}] (* Zerinvary Lajos, Jul 09 2009 *)
PROG
(PARI) a(n) = n!*fibonacci(n); \\ Michel Marcus, Oct 30 2015
(Magma) [Factorial(n)*Fibonacci(n): n in [0..30]]; // G. C. Greubel, Nov 20 2022
(SageMath) [fibonacci(n)*factorial(n) for n in range(31)] # G. C. Greubel, Nov 20 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from James Sellers, Dec 24 1999
STATUS
approved