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URL: https://oeis.org/A184879

⇱ A184879 - OEIS

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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.
2
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
0,5
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.
EXAMPLE
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;
PROG
(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
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Paul Barry, Jan 24 2011
EXTENSIONS
Edited by Klaus Brockhaus, Feb 10 2011
STATUS
approved