A135256 A triangular sequence based on a further generalization of the Cornelius-Schultz matrix polynomials to two sequences in i and j. a(n)=(n-1)!/f[n]: f[n]-> Fibonacci numbers; c(n)=1/n; B(i,j)=(-1)^(i + j)*a[j + 1]*c[i + 1]/(j!*(i - j)!) as a lower triangular matrix.

1, 2, -1, 12, -8, 1, 144, -108, 20, -1, 3600, -2844, 608, -45, 1, 172800, -140112, 32028, -2768, 93, -1, 15724800, -12922992, 3054660, -283916, 11231, -184, 1, 2641766400, -2186787456, 526105872, -50752548, 2170724, -42143, 352, -1, 808380518400, -671798727936, 163175184288, -16056385560

Offset

1,2

Links

Table of n, a(n) for n=1..40.

E. F. Cornelius Jr. and P. Schultz, Sequences generated by polynomials, Amer. Math. Monthly, No. 2, 2008.

Formula

a(n)=(n-1)!/f[n]: f[n]-> Fibonacci numbers; c(n)=1/n; B(i,j)=(-1)^(i + j)*a[j + 1]*c[i + 1]/(j!*(i - j)!) as lower triangular t(n,m)=Coefficients of characteristic polynomials of the inverse of B(i,j)

Example

1;
2, -1;
12, -8, 1;
144, -108,20, -1;
3600, -2844, 608, -45, 1;
172800, -140112, 32028, -2768, 93, -1;
15724800, -12922992, 3054660, -283916, 11231, -184, 1;

Crossrefs

Sequence in context: A058843 A343861 A130559 * A090586 A268512 A217109

Adjacent sequences: A135253 A135254 A135255 * A135257 A135258 A135259

Keyword

uned,sign,tabl

Author

Roger L. Bagula, Feb 13 2008

Status

approved