%I
%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*(n1)!; b[n]=(n1)!; 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*(n1)!; b[n]=(n1)!; 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
