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

0,2

Comments

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

Links

Table of n, a(n) for n=0..65.

Formula

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

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

T(n,2*k) = (-1)^k*binomial(n-k-1,k-1)*(2*n-3*k)/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).

Example

Triangle begins:
  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. A000045, A040000, A057079, A110813, A129710, A191662.

Sequence in context: A192011 A152855 A218907 * A029401 A086150 A105166

Adjacent sequences: A192572 A192573 A192574 * A192576 A192577 A192578

Keyword

sign,tabl,easy

Author

Paul Curtz, Jul 04 2011

Status

approved