A127777 A127773 * A002260 as infinite lower triangular matrices.

1, 3, 6, 6, 12, 18, 10, 20, 30, 40, 15, 30, 45, 60, 75, 21, 42, 63, 84, 105, 126, 28, 56, 84, 112, 140, 168, 196, 36, 72, 108, 144, 180, 216, 252, 288, 45, 90, 135, 180, 225, 270, 315, 360, 405, 55, 110, 165, 220, 275, 330, 385, 440, 495, 550, 66, 132, 198

Offset: 1

Author

Gary W. Adamson, Jan 28 2007

Keywords

• nonn
• tabl
• easy

Comments

Triangular number transform of A002260.

Swapped order of the factors: A002260 * A127773 = A127778.

Examples

			First few rows of the triangle:
   1;
   3,  6;
   6, 12, 18;
  10, 20, 30, 40;
  15, 30, 45, 60, 75;
  ...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000217, A127773, A000537 (row sums), A127778.

Programs

Maple

T(n,k):=piecewise(k<=n,k*binomial(n+1,n-1),nMircea Merca, Apr 11 2012

Mathematica

Table[k*Binomial[n+1,n-1],{n,20},{k,n}]//Flatten (* Harvey P. Dale, Oct 26 2016 *)

Formula

T(n,k) = k*binomial(n+1,n-1) = Sum_{i=1..k} i*binomial(k,i)*binomial(n+2-k,n-i), 1 <= k <= n. - Mircea Merca, Apr 11 2012

Extensions

More terms from Harvey P. Dale, Oct 26 2016