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A085283
a(n) = n*n^n - (n-1)(n-1)^n.
1
1, 1, 7, 65, 781, 11529, 201811, 4085185, 93864121, 2413042577, 68618940391, 2138428376721, 72470493235141, 2653457921150425, 104382202543721467, 4390455017903519489, 196621779843659466481, 9340717969198079777313
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
A007778(n-1)*x(0) = A007778(n)*x(n+1) + a(n),
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
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
Sequence in context: A378691 A355163 A300488 * A069015 A097819 A152525
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 26 2003
STATUS
approved