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

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..118.

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

Sequence in context: A162781 A056975 A294079 * A144435 A182533 A173120

Adjacent sequences: A114114 A114115 A114116 * A114118 A114119 A114120

Keyword

easy,sign,tabl

Author

Paul Barry, Nov 13 2005

Status

approved