OFFSET
1,1
COMMENTS
a(n) = Determinant(A + A^2 + A^3 + A^4 + A^5 + ... + 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*(8*x^6 -50*x^4 +64*x^3 -25*x^2 +1) / ((x -1)^2*(2*x -1)^2*(2*x^2 -5*x +1)^2). - Colin Barker, Jul 13 2014
EXAMPLE
a(1) = Determinant(A) = 2! = 2.
MAPLE
seq(Determinant(sum(A2^i, 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))) \\ 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