A192575 Triangle T(n,0) = A040000(n), T(n,k)=0 (odd-numbered columns); T(n,k) = (-1)^(k/2)*A110813(n-k/2-1,k/2-1) (even-numbered columns, k>0).

1, 2, 0, 2, 0, -1, 2, 0, -3, 0, 2, 0, -5, 0, 1, 2, 0, -7, 0, 4, 0, 2, 0, -9, 0, 9, 0, -1, 2, 0, -11, 0, 16, 0, -5, 0, 2, 0, -13, 0, 25, 0, -14, 0, 1, 2, 0, -15, 0, 36, 0, -30, 0, 6, 0, 2, 0, -17, 0, 49, 0, -55, 0, 20, 0, -1

Offset: 0

Author

Paul Curtz, Jul 04 2011

Keywords

• sign
• tabl
• easy

Comments

A zero-padded variant of A110813, which provides more information.

Examples

			1;
2 0;
2 0  -1;
2 0  -3 0;
2 0  -5 0  1;
2 0  -7 0  4 0;
2 0  -9 0  9 0  -1;
2 0 -11 0 16 0  -5 0;
2 0 -13 0 25 0 -14 0 1;
2 0 -15 0 36 0 -30 0 6 0;
		

Crossrefs

Cf. A191662.

Formula

T(n,k) = T(n-1,k)-T(n-2,k-2), n>1.

T(n,2k+1)=0.

T(n,2k) = (-1)^k*binomial(n-k-1,k-1)*(2n-3k)/k , k>0. - R. J. Mathar, Aug 26 2011

T(n,0) = A040000(n).

sum_{k=0..n} T(n,k) = A057079(n).

sum_{k=0..n} |T(n,k)| = A000045(n+2). (See A129710).