A184879 Triangular array T read by rows: T(n, k) = Sum_{i=0..2*n-2*k} binomial(2*n-2*k, i)*binomial(2*k, i)*(-1)^i, 0 <= k <= n.

1, 1, 1, 1, -2, 1, 1, -1, -1, 1, 1, 4, 6, 4, 1, 1, 13, 2, 2, 13, 1, 1, 26, -17, -20, -17, 26, 1, 1, 43, -39, -5, -5, -39, 43, 1, 1, 64, -36, 64, 70, 64, -36, 64, 1, 1, 89, 36, 116, 14, 14, 116, 36, 89, 1, 1, 118, 237, 8, -238, -252, -238, 8, 237, 118, 1, 1, 151, 643, -395, -358

Offset: 0

Author

Paul Barry, Jan 24 2011

Keywords

• sign
• tabl

Comments

Row sums are in A108474, antidiagonal sums are in A184880.

T(2*n, n) is (-1)^n*A000984, T(2*n ,n)-T(2*n, n+1) is A184881.

Examples

			Triangle begins
  1;
  1,   1;
  1,  -2,   1;
  1,  -1,  -1,   1;
  1,   4,   6,   4,    1;
  1,  13,   2,   2,   13,    1;
  1,  26, -17, -20,  -17,   26,    1;
  1,  43, -39,  -5,   -5,  -39,   43,   1;
  1,  64, -36,  64,   70,   64,  -36,  64,   1;
  1,  89,  36, 116,   14,   14,  116,  36,  89,   1;
  1, 118, 237,   8, -238, -252, -238,   8, 237, 118,   1;
		

Crossrefs

Cf. A007318, A000984, A108474, A184880, A184881.

Programs

Magma

&cat[ [ &+[ Binomial(2*n-2*k, i)*Binomial(2*k, i)*(-1)^i: i in [0..(2*n-2*k)] ]: k in [0..n] ]: n in [0..11] ]; // Klaus Brockhaus, Feb 10 2011

Extensions

Edited by Klaus Brockhaus, Feb 10 2011