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

1,2

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

Links

Table of n, a(n) for n=1..66.

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

Example

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;
  ...

Maple

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

Crossrefs

Cf. A083706, A130296, A130300.

Sequence in context: A347066 A099375 A348835 * A133601 A258207 A133094

Adjacent sequences: A130298 A130299 A130300 * A130302 A130303 A130304

Keyword

nonn,tabl

Author

Gary W. Adamson, May 20 2007

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

Status

approved