A114117 Inverse of 1's counting matrix A114116.

1, 0, 1, -2, 1, 1, -1, -1, 1, 1, 0, -2, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, 0, -2, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 1

Offset

0,4

Comments

Row sums are (1,1,0,0,0,.....) with g.f. 1+x. Diagonal sums have g.f. (1-x^2-x^3)/(1-x^3). Product of A114115 and the first difference matrix (1-x,x).

Links

Table of n, a(n) for n=0..119.

Formula

T(n, k) = Sum_{j=0..n} Sum_{i=0..n} C(floor((n+i)/2), j)*C(j, floor((n+i)/2))*(2*C(0, j-k)-C(1, j-k)).

Example

Triangle begins
  1;
  0, 1;
 -2, 1, 1;
 -1,-1, 1, 1;
  0,-2, 0, 1, 1;
  0,-1,-1, 0, 1, 1;
  0, 0,-2, 0, 0, 1, 1;
  0, 0,-1,-1, 0, 0, 1, 1;

Crossrefs

Cf. A114115, A114116.

Sequence in context: A370482 A294079 A375669 * A144435 A182533 A173120

Adjacent sequences: A114114 A114115 A114116 * A114118 A114119 A114120

Keyword

easy,sign,tabl

Author

Paul Barry, Nov 13 2005

Status

approved