A130460 Infinite lower triangular matrix,(1,0,0,0,...) in the main diagonal and (1,2,3,...) in the subdiagonal.

1, 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

Offset: 1

Author

Gary W. Adamson, May 28 2007

Keywords

• nonn
• tabl

Comments

Given M = this sequence as an infinite lower triangular matrix and V = any sequence as a column vector, then M*V is the concatenation of the first term of V with the dot product of (1, 2, 3, ...) and V.

Examples

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

Crossrefs

Cf. A130461, A130476, A130477, A130478.

Formula

A natural number operator as an infinite lower triangular matrix M. (1,0,0,0,...) in the main diagonal, (1,2,3,...) in the subdiagonal and the rest zeros.

Extensions

a(5) corrected by Gionata Neri, Jun 22 2016