[go: up one dir, main page]

login
A158047
Determinant of power series with alternate signs of gamma matrix with determinant 4!.
1
24, 144, 13896, 842400, 36604920, 2333944368, 126441557448, 6680853691200, 387982670513688, 20676854461594320, 1158249535425969384, 63778918790403180000, 3507499386329443453752, 194248225087593045241968
OFFSET
0,1
COMMENTS
a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n)
where A is the submatrix A(1..5,1..5) 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.
EXAMPLE
a(1) = Determinant(A) = 4! = 24.
MAPLE
seq(Determinant(sum(A^i*(-1)^(i-1), i=1..n)), n=1..30);
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved