A134402 Triangle read by rows, for n > 0, n zeros followed by n.

1, 0, 1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13

Offset

0,6

Comments

Multiplied by the vector [1, 2, 3, ...] from the right gives (1, 2, 6, 12, 20, 30, 42, ...), A002378.

Triangle T(n,k), read by rows, given by [0,0,0,0,0,0,0,...] DELTA [1,1,-1,1,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 26 2007

Links

Table of n, a(n) for n=0..104.

Formula

Triangle read by rows, a(0) = 1, then for n > 0, n zeros followed by n. Infinite lower triangular matrix with (1, 1, 2, 3, 4, ...) in the main diagonal and the rest zeros.

G.f.: (1-x*y+x^2*y^2)/(-1+x*y)^2. - R. J. Mathar, Aug 11 2015

Example

First few rows of the triangle:
  1;
  0, 1;
  0, 0, 2;
  0, 0, 0, 3;
  0, 0, 0, 0, 4;
  0, 0, 0, 0, 0, 5;
  ...

Mathematica

Join[{1}, Flatten[Table[PadLeft[{n}, n+1, 0], {n, 15}]]] (* Harvey P. Dale, May 08 2012 *)

Crossrefs

Cf. A134403, A005449.

Essentially the same as A130460.

Sequence in context: A130460 A132440 A218272 * A174712 A127647 A325458

Adjacent sequences: A134399 A134400 A134401 * A134403 A134404 A134405

Keyword

nonn,easy,tabl

Author

Gary W. Adamson, Oct 23 2007

Status

approved