A128132 A natural number transform, companion to A127701.

1, -1, 2, 0, -1, 3, 0, 0, -1, 4, 0, 0, 0, -1, 5, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 0, -1, 7, 0, 0, 0, 0, 0, 0, -1, 8, 0, 0, 0, 0, 0, 0, 0, -1, 9, 0, 0, 0, 0, 0, 0, 0, 0, -1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 12

Offset: 1

Author

Gary W. Adamson, Feb 15 2007

Keywords

• tabl
• sign
• easy

Comments

Binomial transform is A128133.

Examples

			Triangle T(n,k) (with rows n >= 1 and columns k = 1..n) begins:
   1;
  -1,  2;
   0, -1,  3;
   0,  0, -1,  4;
   0,  0,  0, -1,  5;
   0,  0,  0,  0, -1, 6;
   ...
		

Crossrefs

Cf. A127701, A128133, A128134.

Programs

Maple

A128132 := proc(n,k)
    if n = k then
        n;
    elif k = n-1 then
        -1 ;
    else
        0 ;
    end if;
end proc: # R. J. Mathar, Apr 26 2016

Mathematica

{1}~Join~Table[PadLeft[{-1, n}, n], {n, 2, 12}] // Flatten (* Michael De Vlieger, Apr 26 2016 *)

Formula

T(n,n) = n.

T(n,n-1) = -1.

T(n,k) = 0 for k <> n, n-1.