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A174963 - OEIS
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A174963
Determinant of the symmetric n X n matrix M_n where M_n(j,k) = n for j = k, M_n(j,n) = n-j, M_n(n,k) = n-k, M_n(j,k) = 0 otherwise.
2
1, 3, 12, 32, -625, -24624, -705894, -19922944, -588305187, -18500000000, -622498190424, -22414085849088, -862029149531797, -35320307409809408, -1537494104003906250, -70904672533321089024, -3454944623172347662151, -177423154932124201844736
OFFSET
1,2
REFERENCES
J.-M. Monier, Algèbre et géometrie, exercices corrigés. Dunod, 1997, p. 78.
LINKS
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
Cf. A174962.
Sequence in context: A365738 A288605 A268768 * A054602 A083725 A192972
KEYWORD
sign
AUTHOR
Michel Lagneau, Apr 02 2010
EXTENSIONS
Edited by Klaus Brockhaus, Apr 11 2010
STATUS
approved