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

0,9

Comments

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

Links

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

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

Example

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.

Sequence in context: A177517 A227819 A064287 * A128206 A371417 A103294

Adjacent sequences: A196386 A196387 A196388 * A196390 A196391 A196392

Keyword

nonn,tabl,easy

Author

Philippe Deléham, Oct 28 2011

Status

approved