OFFSET
0,3
COMMENTS
The system of equations
x(0) = n*x(1) + 1,
(n-1)*x(1) = n*x(2) + 1,
...
(n-1)*x(n) = n*x(n+1) + 1.
relates to the Monkey-And-Coconuts problem and reduces to the single equation
whose solutions {x(0),x(n+1)} are given by {A014293(n), A085606(n)=A007778(n-1) - 1}. - Lekraj Beedassy, Jul 15 2003
For n >= 1, a(n) is equal to the number of functions f: {1,2,...,n+1}->{1,2,...,n} such that Im(f) contains a fixed element. - Aleksandar M. Janjic and Milan Janjic, Feb 27 2007
LINKS
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
K. Belcourt, How Many Coconuts
Santo D'Agostino, “The Coconut Problem”; Updated With Solution, May 2011.
J. Dean, Sailors, monkey and coconuts
A. K. Dewdney, The Monkey and the Coconuts
G. Lewandrowski, The Monkey Problem
R. Raja, Monkeys and Coconuts
A. Rishi, Nemo's sailors and the monkey
Dr. Rob, The MathForum, Coconut piles
D. J. Wright, Five Pirates and a Monkey
FORMULA
E.g.f.: -(x + 2*x*W(-x) + W(-x)^2)/(W(-x)*(1 + W(-x))^3), where W(x) is the Lambert W function. - Fabian Pereyra, Sep 26 2023
MATHEMATICA
Join[{1}, Table[n*n^n-(n-1)(n-1)^n, {n, 20}]] (* Harvey P. Dale, Sep 08 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 26 2003
STATUS
approved