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.

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

(list; table; graph; refs; listen; history; text; internal format)

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.

LINKS

Table of n, a(n) for n=0..70.

EXAMPLE

Triangle begins

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

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

Sequence in context: A146532 A305720 A225372 * A373201 A119335 A155869

Adjacent sequences: A184876 A184877 A184878 * A184880 A184881 A184882

KEYWORD

sign,tabl

AUTHOR

Paul Barry, Jan 24 2011

EXTENSIONS

Edited by Klaus Brockhaus, Feb 10 2011

STATUS

approved