A117389 A skew Delannoy number triangle read by rows.

1, 0, 1, 0, 1, 1, 0, 0, 3, 1, 0, 0, 1, 5, 1, 0, 0, 0, 5, 7, 1, 0, 0, 0, 1, 13, 9, 1, 0, 0, 0, 0, 7, 25, 11, 1, 0, 0, 0, 0, 1, 25, 41, 13, 1, 0, 0, 0, 0, 0, 9, 63, 61, 15, 1, 0, 0, 0, 0, 0, 1, 41, 129, 85, 17, 1

Offset: 0

Author

Paul Barry, Mar 11 2006

Keywords

• easy
• nonn
• tabl

Comments

Row sums are the trinomial numbers A000073(n+2). Diagonal sums are A079973.

Examples

			Triangle begins
1,
0, 1,
0, 1, 1,
0, 0, 3, 1,
0, 0, 1, 5, 1,
0, 0, 0, 5, 7, 1,
0, 0, 0, 1, 13, 9, 1,
0, 0, 0, 0, 7, 25, 11, 1
		

Crossrefs

Cf. A008288.

Formula

Number triangle T(n,k)=[k<=n]*sum{j=0..2k-n, C(2k-n,j)C(n-k,j)2^j}; T(n,k)=sum{j=0..2k-n, C(2k-n,j)C(n-k,n-k-j)2^j};