OFFSET
0,2
COMMENTS
REFERENCES
F.J. MacWilliams, N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 2003, p. 321.
FORMULA
T(n, k) = Sum_{j=0..n-k} (-1)^j*C(j+k-2, j).
T(n, k) = Sum_{j=0..n-k} (-1)^(n-k-j)*C(n-j-2, n-j-k).
T(n, k) = Sum_{j=k..n} (-1)^(n-j)*C(n, j)*(2^(j-k+1)-1).
EXAMPLE
Triangle begins
1;
2,1;
2,1,1;
2,1,0,1;
2,1,1,-1,1;
2,1,0,2,-2,1;
MATHEMATICA
T[n_, k_] := Sum[(-1)^(n-j) Binomial[n, j] (2^(j-k+1) - 1), {j, k, n}]; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 27 2017 *)
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Oct 25 2005
STATUS
approved