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

0,5

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.

Links

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

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)}.

Example

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

Crossrefs

Sequence in context: A363970 A356113 A188461 * A173046 A173043 A082046

Adjacent sequences: A188471 A188472 A188473 * A188475 A188476 A188477

Keyword

nonn,easy,tabl

Author

Paul Barry, Apr 01 2011

Status

approved