A117941 Inverse of number triangle A117939.

1, -2, 1, -5, 2, 1, -2, 0, 0, 1, 4, -2, 0, -2, 1, 10, -4, -2, -5, 2, 1, -5, 0, 0, 2, 0, 0, 1, 10, -5, 0, -4, 2, 0, -2, 1, 25, -10, -5, -10, 4, 2, -5, 2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, -2, 0, 0, 0, 0, 0, 0, 0, -2, 1, 10, -4, -2, 0, 0, 0, 0, 0, 0, -5, 2, 1, 4, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1, -8, 4, 0, 4, -2, 0, 0, 0, 0, 4, -2, 0, -2, 1

Offset: 0

Author

Paul Barry, Apr 05 2006

Keywords

• sign
• tabl

Comments

Row sums are A117942.

T(n, k) mod 2 = A117944(n,k).

Examples

			Triangle begins
   1;
  -2,   1;
  -5,   2,  1;
  -2,   0,  0,   1;
   4,  -2,  0,  -2, 1;
  10,  -4, -2,  -5, 2, 1;
  -5,   0,  0,   2, 0, 0,  1;
  10,  -5,  0,  -4, 2, 0, -2, 1;
  25, -10, -5, -10, 4, 2, -5, 2, 1;
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A117939, A117942, A117944.

Programs

Mathematica

M[n_, k_]:= M[n, k]= If[k>n, 0, Sum[JacobiSymbol[Binomial[n, j], 3]*JacobiSymbol[Binomial[n-j, k], 3], {j,0,n}], 0];
m:= m= With[{q = 60}, Table[M[n, k], {n,0,q}, {k,0,q}]];
T[n_, k_]:= Inverse[m][[n+1, k+1]];
Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten (* G. C. Greubel, Oct 29 2021 *)