A196389 Triangle T(n,k), read by rows, given by (0,1,-1,0,0,0,0,0,0,0,...) DELTA (1,0,0,1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.

1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 0, 3, 1, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1

Offset: 0

Author

Philippe Deléham, Oct 28 2011

Keywords

• nonn
• tabl
• easy

Comments

Row sums are A028310; diagonal sums are A057979; column sums are A000027.

Examples

			Triangle begins:
  1;
  0, 1;
  0, 1, 1;
  0, 0, 2, 1;
  0, 0, 0, 3, 1;
  0, 0, 0, 0, 4, 1;
  0, 0, 0, 0, 0, 5, 1;
  0, 0, 0, 0, 0, 0, 6, 1;
  0, 0, 0, 0, 0, 0, 0, 7, 1;
  0, 0, 0, 0, 0, 0, 0, 0, 8, 1;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1; ...
		

Crossrefs

Cf. A084938.

Formula

T(n,n)=1, T(n+1,n)=n.

G.f.: (1-x*y+x^2*y)/(1-x*y)^2. - Philippe Deléham, Oct 31 2011

Sum_{k=0..n} T(n,k)*x^k = A000007(n), A028310(n), A057711(n+1), A064017(n+1) for x = 0, 1, 2, 3 respectively. - Philippe Deléham, Oct 31 2011