A130301 Triangle read by rows: A130296 * A007318, as infinite lower triangular matrices.

1, 3, 1, 5, 3, 1, 7, 6, 4, 1, 9, 10, 10, 5, 1, 11, 15, 20, 15, 6, 1, 13, 21, 35, 35, 21, 7, 1, 15, 28, 56, 70, 56, 28, 8, 1, 17, 36, 84, 126, 126, 84, 36, 9, 1, 19, 45, 120, 210, 252, 210, 120, 45, 10, 1, 21, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1

Offset: 1

Author

Gary W. Adamson, May 20 2007

Keywords

• nonn
• tabl

Comments

Row sums = A083706: (1, 4, 9, 18, 35, 68, ...).

A130300 = A007318 * A130296.

The lower triangular matrix A130296 is equal to the restriction of the square array A051340 to its lower left triangular part. So this is also equal to (A051340) * A007318, where (A051340) is the lower triangular part of A051340, i.e., A051340[i,j] replaced by zero for j > i: see Mathar's Maple code. - M. F. Hasler, Aug 15 2015

Examples

			First few rows of the triangle:
   1;
   3,  1;
   5,  3,  1;
   7,  6,  4,  1;
   9, 10, 10,  5,  1;
  11, 15, 20, 15,  6,  1;
  13, 21, 35, 35, 21,  7,  1;
  ...
		

Crossrefs

Cf. A083706, A130296, A130300.

Programs

Maple

A130301 := proc(n, k)
    add( A051340(n, i)*binomial(i, k), i=k..n);
end proc: # R. J. Mathar, Jul 16 2015

Formula

A130301[m,n] = A121775[m,n] for n >= m/2. A130301[m,1] = 2m-1, A130301[m,2] = A000217[m-1], A130301[m,m] = 1, A130301[m,m-1] = m for m>2. - M. F. Hasler, Aug 15 2015

Extensions

Corrected (missing a(15)=1 inserted) by M. F. Hasler, Aug 15 2015

a(26) = 27 corrected and more terms from Georg Fischer, May 29 2023