A104727 Triangle T(n,k) = (k-1-n)*(k-2-n)*(k^2+k+2*k*n+3*n^2+5*n)/24 read by rows, 1<=k<=n.

1, 7, 3, 25, 15, 6, 65, 45, 26, 10, 140, 105, 71, 40, 15, 266, 210, 155, 103, 57, 21, 462, 378, 295, 215, 141, 77, 28, 750, 630, 511, 395, 285, 185, 100, 36, 1155, 990, 826, 665, 510, 365, 235, 126, 45, 1705, 1485, 1266, 1050, 840, 640, 455, 291, 155, 55, 2431, 2145, 1860, 1578, 1302, 1036, 785, 555, 353, 187, 66, 3367, 3003

Offset: 1

Author

Gary W. Adamson, Mar 20 2005

Keywords

• nonn
• easy
• tabl

Comments

The triangle is created by multiplying the lower triangular matrix A(n,k) = A000217(k) (1<=k<=n) by the lower triangular matrix B(n,k) = n-k+1 (1<=k<=n): T(n,k) = sum_{j=k..n} A(n,j)*B(j,k).

The commuted product B * A generates triangle A098358.

Examples

			First few rows of the triangle are:
1;
7, 3;
25, 15, 6;
665, 45, 26, 10;
140, 105, 71, 40, 15;
266, 210, 155, 103, 57, 21;
...
		

Crossrefs

Cf. A098358, A104727, A024166 (row sums).

Formula

T(n,1) = A001296(n). - R. J. Mathar, Oct 29 2011