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
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;
Programs
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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
Comments