A188474 A generalized Deutsch triangle.

1, 1, 1, 1, 5, 1, 1, 10, 10, 1, 1, 16, 40, 16, 1, 1, 23, 102, 102, 23, 1, 1, 31, 209, 393, 209, 31, 1, 1, 40, 376, 1122, 1122, 376, 40, 1, 1, 50, 620, 2656, 4296, 2656, 620, 50, 1, 1, 61, 960, 5536, 13100, 13100, 5536, 960, 61, 1, 1, 73, 1417, 10522, 34036, 50180, 34036, 10522, 1417, 73, 1

Offset: 0

Author

Paul Barry, Apr 01 2011

Keywords

• nonn
• easy
• tabl

Comments

Member r=2 of the family of "Pascal-like" triangles with T(n,k)=sum{j=0..n-k+1, (j/(n+2-j))*C(n+2-j,n-k+1)*C(n+2-j,k+1)*r^(j-1)}.

The Deutsch triangle A100754 corresponds to r=1.

Row sums are A137398(n+1) (conjecture). Diagonal sums are A188476.

Examples

			Triangle begins
1,
1, 1,
1, 5, 1,
1, 10, 10, 1,
1, 16, 40, 16, 1,
1, 23, 102, 102, 23, 1,
1, 31, 209, 393, 209, 31, 1,
1, 40, 376, 1122, 1122, 376, 40, 1,
1, 50, 620, 2656, 4296, 2656, 620, 50, 1,
1, 61, 960, 5536, 13100, 13100, 5536, 960, 61, 1,
1, 73, 1417, 10522, 34036, 50180, 34036, 10522, 1417, 73, 1
		

Formula

T(n,k)=sum{j=0..n-k+1, (j/(n+2-j))*C(n+2-j,n-k+1)*C(n+2-j,k+1)*2^(j-1)}.