A124847 Triangle read by rows: T(n,k) = k(k+1)*binomial(n-1, k-1)/2 (1 <= k <= n).

1, 1, 3, 1, 6, 6, 1, 9, 18, 10, 1, 12, 36, 40, 15, 1, 15, 60, 100, 75, 21, 1, 18, 90, 200, 225, 126, 28, 1, 21, 126, 350, 525, 441, 196, 36, 1, 24, 168, 560, 1050, 1176, 784, 288, 45, 1, 27, 216, 840, 1890, 2646, 2352, 1296, 405, 55, 1, 30, 270, 1200, 3150, 5292, 5880

Offset: 1

Author

Gary W. Adamson, Nov 10 2006

Keywords

• nonn
• tabl

Comments

Sum of row n gives A049611(n).

Triangle is P*A, where P is the Pascal triangle written as a lower triangular matrix and C is the diagonal matrix of the triangular numbers 1, 3, 6, 10, ....

Examples

			First few rows of the triangle:
  1;
  1,   3;
  1,   6,   6;
  1,   9,  18,  10;
  1,  12,  36,  40,  15;
  1,  15,  60, 100,  75,  21;
  ...
Sum of row 3 = 38 = (1 + 9 + 18 + 10) = A049611(3).
		

Crossrefs

Cf. A049611.

Programs

Maple

T:=(n,k)->k*(k+1)*binomial(n-1,k-1)/2: for n from 1 to 12 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form

Extensions

Edited by N. J. A. Sloane, Nov 24 2006