A213953 Triangle by rows, inverse of A208891.

1, -1, 1, 0, -1, 1, 1, -1, -1, 1, 1, 1, -2, -1, 1, -2, 5, 0, -3, -1, 1, -9, 5, 10, -2, -4, -1, 1, -9, -21, 25, 15, -5, -5, -1, 1, 50, -105, -11, 62, 19, -9, -6, -1, 1, 267, -141, -301, 56, 119, 21, -14, -7, -1, 1, 413, 777

Offset: 0

Author

Gary W. Adamson, Jun 26 2012

Keywords

• tabl
• sign

Examples

			Triangle starts:
1;
-1, 1
0, -1, 1
1, -1, -1, 1;
1, 1, -2, -1, 1;
-2, 5, 0, -3, -1, 1;
-9, 5, 10, -2, -4, -1, 1;
-9, -21, 25, 15, -5, -5, -1, 1;
50, -105, -11, 62, 19, -9, -6, -1, 1;
267, -141, -301, 56, 119, 21, -14, -7, -1, 1;
413, 777, -1040, -566, 226, 198, 20, -20, -8, -1, 1;
...
		

Crossrefs

Cf. A208891, A000587 (first column), A014619 (2nd column), A080956 (4th subdiagonal).

Programs

Maple

A208891 := proc(n,k)
    if n <0 or k<0 or k>n then
            0;
    elif n = k then
            1 ;
    else
            binomial(n-1,k) ;
    end if;
end proc:
A259456 := proc(n)
    local A, row, col ;
    A := Matrix(n, n) ;
    for row from 1 to n do
        for col from 1 to n do
            A[row, col] := A208891(row-1,col-1) ;
        end do:
    end do:
    LinearAlgebra[MatrixInverse](A) ;
end proc:
A259456(20) ; # R. J. Mathar, Jul 21 2015

Formula

Inverse of triangle A208891, Pascal's triangle matrix with an appended right border of 1's.