A135281 - OEIS

%I #3 Mar 30 2012 17:34:22

%S 1,-1,-2,2,5,3,-18,-39,-23,-4,1152,2064,872,119,5,-720000,-1122000,

%T -331400,-26755,-719,-6,5598720000,7985952000,1768046400,84475980,

%U 1128024,5039,7,-658683809280000,-887001391584000,-157639245422400,-4880494582740,-33169857336,-63204617,-40319,-8

%N A triangular sequence based on a two sequence lower triangular matrix. a(n)=(-1)^n*(n-1)!; b[n]=(n-1)!; M(i,j)={{a(i),b(j)},{b(j),a(i+1)}}; a0(i,j)=Det[M(i,j)]; This method gives an tridiagonal matrix effect to a lower triangular matrix base.

%C (n+2) factor is added to get the Integer result instead of a rational result in the polynomials.

%F a(n)=(-1)^n*(n-1)!; b[n]=(n-1)!; m(i,j)=If[i > j, (-1)^(i + j)*((a[j + 1]*a[j + 2] - b[i + 1]^2)/(n + 1)!)/(j!*(i - j)!), 0] t(n,m)=(n+2)*Coefficients of Characteristic polynomials of inverse of m(i,j)

%e {1},

%e {-1, -2},

%e {2, 5, 3},

%e {-18, -39, -23, -4},

%e {1152, 2064, 872,119, 5},

%e {-720000, -1122000, -331400, -26755, -719, -6},

%e {5598720000, 7985952000, 1768046400, 84475980,1128024, 5039, 7},

%K uned,sign

%O 1,3

%A _Roger L. Bagula_, Feb 15 2008