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.

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

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

Cf. A174962.

Sequence in context: A365738 A288605 A268768 * A054602 A083725 A192972

Adjacent sequences: A174960 A174961 A174962 * A174964 A174965 A174966

Keyword

sign

Author

Michel Lagneau, Apr 02 2010

Extensions

Edited by Klaus Brockhaus, Apr 11 2010

Status

approved