A104734 Triangle T(n,k) = sum_{j=k..n} (2n-2j+1)*binomial(k,j-k), read by rows, 0<=k<=n.

1, 3, 1, 5, 4, 1, 7, 8, 5, 1, 9, 12, 12, 6, 1, 11, 16, 20, 17, 7, 1, 13, 20, 28, 32, 23, 8, 1, 15, 24, 36, 48, 49, 30, 9, 1, 17, 28, 44, 64, 80, 72, 38, 10, 1, 19, 32, 52, 80, 112, 129, 102, 47, 11, 1, 21, 36, 60, 96, 144, 192, 201, 140, 57, 12, 1, 23, 40, 68, 112, 176, 256, 321, 303, 187, 68, 13, 1, 25, 44, 76, 128, 208, 320, 448, 522, 443, 244, 80, 14, 1

Offset

0,2

Comments

Array A210489 (without first row) read downwards antidiagonals. - R. J. Mathar, Sep 17 2013

Links

Table of n, a(n) for n=0..90.

Formula

Matrix product of the triangle A = A099375 by B = [1; 0, 1; 0, 1, 1; 0, 0, 2, 1; 0, 0, 1, 3, 1;...] (which is the triangular view of A026729).

Example

First few rows of the triangle are:
1;
3, 1;
5, 4, 1;
7, 8, 5, 1;
9, 12, 12, 6, 1;
11, 16, 20, 17, 7, 1;
...

Crossrefs

Cf. A001891 (row sums), A026729.

Sequence in context: A290534 A242639 A117853 * A029655 A110813 A124883

Adjacent sequences: A104731 A104732 A104733 * A104735 A104736 A104737

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 20 2005

Status

approved