A125026 Triangle read by rows: T(n,k) = k*binomial(n,k) + binomial(n-1,k) (1 <= k <= n).

1, 3, 2, 5, 7, 3, 7, 15, 13, 4, 9, 26, 34, 21, 5, 11, 40, 70, 65, 31, 6, 13, 57, 125, 155, 111, 43, 7, 15, 77, 203, 315, 301, 175, 57, 8, 17, 100, 308, 574, 686, 532, 260, 73, 9, 19, 126, 444, 966, 1386, 1344, 876, 369, 91, 10, 21, 155, 615, 1530, 2562, 2982, 2430, 1365

Offset: 1

Author

Gary W. Adamson, Nov 15 2006

Keywords

• nonn
• tabl

Comments

Also A007318 * A127899 (unsigned) as a product of two infinite lower triangular matrices. - Gary W. Adamson, Feb 19 2007

Examples

			First few rows of the triangle are
   1;
   3,   2;
   5,   7,   3;
   7,  15,  13,   4;
   9,  26,  34,  21,   5;
  11,  40,  70,  65,  31,   6;
  13,  57, 125, 155, 111,  43,  7;
  ...
		

Crossrefs

Cf. A099035 (row sums).

Programs

Maple

T:=(n,k)->k*binomial(n,k)+binomial(n-1,k): 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 29 2006