A134399 Matrix product of Binomial triangle A007318 and triangle with (1, 1, 2, 3, 4, 5, ...) in the main diagonal and the rest zeros.

1, 1, 1, 1, 2, 2, 1, 3, 6, 3, 1, 4, 12, 12, 4, 1, 5, 20, 30, 20, 5, 1, 6, 30, 60, 60, 30, 6, 1, 7, 42, 105, 140, 105, 42, 7, 1, 8, 56, 168, 280, 280, 168, 56, 8, 1, 9, 72, 252, 504, 630, 504, 252, 72, 9

Offset: 0

Author

Gary W. Adamson, Oct 23 2007

Keywords

• nonn
• tabl

Comments

Row sums = A005183: (1, 2, 5, 13, 33, 81, 193, ...).

Examples

			First few rows of the triangle:
  1;
  1, 1;
  1, 2,  2;
  1, 3,  6,   3;
  1, 4, 12,  12,   4;
  1, 5, 20,  30,  20,   5;
  1, 6, 30,  60,  60,  30,  6;
  1, 7, 42, 105, 140, 105, 42, 7;
  ...
		

Crossrefs

Cf. A005183, A007318.

Programs

Mathematica

Table[Max[k, 1]*Binomial[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, May 03 2024 *)

Formula

T(n,0) = 1; T(n,k) = k*binomial(n,k) for 1 <= k <= n. [corrected by Paolo Xausa, May 03 2024]

Extensions

Corrected and edited by Olivier Gérard, Aug 01 2013