A104731 Triangle T(n,k) = sum_{j=k..n} (j+1)*binomial(k,j-k), read by rows, 0<=k<=n.

1, 1, 2, 1, 5, 3, 1, 5, 11, 4, 1, 5, 16, 19, 5, 1, 5, 16, 37, 29, 6, 1, 5, 16, 44, 71, 41, 7, 1, 5, 16, 44, 103, 121, 55, 8, 1, 5, 16, 44, 112, 211, 190, 71, 9, 1, 5, 16, 44, 112, 261, 390, 281, 89, 10, 1, 5, 16, 44, 112, 272, 555, 666, 397, 109, 11

Offset

0,3

Links

Table of n, a(n) for n=0..65.

Formula

Product of the triangles A(n,k) = k+1 and B = binomial(k,n-k) = [1; 0, 1; 0, 1, 1; 0, 0, 2, 1; 0, 0, 1, 3, 1;...], the triangular view of A026729.

Example

The first few rows of the triangle are:
1;
1, 2;
1, 5, 3;
1, 5, 11, 4
1, 5, 16, 19, 5;
1, 5, 16, 37, 29, 6;
...

Crossrefs

Cf. A014286 (row sums), A045925, A026729.

Sequence in context: A177760 A329440 A339494 * A240192 A264751 A209130

Adjacent sequences: A104728 A104729 A104730 * A104732 A104733 A104734

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 20 2005

Status

approved