A135281 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.

1, -1, -2, 2, 5, 3, -18, -39, -23, -4, 1152, 2064, 872, 119, 5, -720000, -1122000, -331400, -26755, -719, -6, 5598720000, 7985952000, 1768046400, 84475980, 1128024, 5039, 7, -658683809280000, -887001391584000, -157639245422400, -4880494582740, -33169857336, -63204617, -40319, -8

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..36.

Formula

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)

Example

{1},
{-1, -2},
{2, 5, 3},
{-18, -39, -23, -4},
{1152, 2064, 872,119, 5},
{-720000, -1122000, -331400, -26755, -719, -6},
{5598720000, 7985952000, 1768046400, 84475980,1128024, 5039, 7},

Crossrefs

Sequence in context: A322786 A184243 A356891 * A068465 A217876 A209771

Adjacent sequences: A135278 A135279 A135280 * A135282 A135283 A135284

Keyword

uned,sign

Author

Roger L. Bagula, Feb 15 2008

Status

approved