OFFSET
1,1
COMMENTS
a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n), where A is the submatrix A(1..3,1..3) of the matrix with factorial determinant
A = [[1,1,1,1,1,1,...], [1,2,1,2,1,2,...], [1,2,3,1,2,3,...], [1,2,3,4,1,2,...], [1,2,3,4,5,1,...], [1,2,3,4,5,6,...], ...]. Note: Determinant A(1..n,1..n) = (n-1)!.
REFERENCES
G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008.
FORMULA
Empirical g.f.: -2*x*(2*x^2 -1)*(4*x^4 -11*x^2 +1) / ((x -1)*(x +1)*(2*x -1)*(2*x +1)*(2*x^2 -5*x +1)*(2*x^2 +5*x +1)). - Colin Barker, Jul 13 2014
EXAMPLE
a(1) = Determinant(A) = 2! = 2.
MAPLE
seq(Determinant(sum(A^i*(-1)^(i-1), i=1..n)), n=1..30);
PROG
(PARI) vector(100, n, matdet(sum(k=1, n, [1, 1, 1 ; 1, 2, 1 ; 1, 2, 3]^k*(-1)^(k-1)))) \\ Colin Barker, Jul 13 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009
EXTENSIONS
More terms, and offset changed to 1 by Colin Barker, Jul 13 2014
STATUS
approved