OFFSET
1,2
REFERENCES
J.-M. Monier, Algèbre et géometrie, exercices corrigés. Dunod, 1997, p. 78.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..100
FORMULA
a(n) = n^n - ((n-1)*n*(2*n-1)/6)*n^(n-2).
EXAMPLE
a(5) = determinant(M_5) = -625 where M_5 is the matrix
[5 0 0 0 4]
[0 5 0 0 3]
[0 0 5 0 2]
[0 0 0 5 1]
[4 3 2 1 5]
MAPLE
with(numtheory):for n from 1 to 25 do:x:=n^n -((n-1)*n*(2*n-1)/6)*n^(n-2):print(x):od:
PROG
(Magma) [ n^n -((n-1)*n*(2*n-1)/6)*n^(n-2): n in [1..18] ]; // Klaus Brockhaus, Apr 11 2010
(Magma) [ Determinant( SymmetricMatrix( &cat[ [ i lt j select 0 else n: i in [1..j] ]: j in [1..n-1] ] cat [ 1+((n-1-k) mod n): k in [1..n] ] ) ): n in [1..18] ]; // Klaus Brockhaus, Apr 11 2010
CROSSREFS
KEYWORD
sign
AUTHOR
Michel Lagneau, Apr 02 2010
EXTENSIONS
Edited by Klaus Brockhaus, Apr 11 2010
STATUS
approved