A188474 - OEIS

%I #6 Mar 30 2012 18:59:29

%S 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,

%T 209,31,1,1,40,376,1122,1122,376,40,1,1,50,620,2656,4296,2656,620,50,

%U 1,1,61,960,5536,13100,13100,5536,960,61,1,1,73,1417,10522,34036,50180,34036,10522,1417,73,1

%N A generalized Deutsch triangle.

%C 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)}.

%C The Deutsch triangle A100754 corresponds to r=1.

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

%F 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)}.

%e Triangle begins

%e 1,

%e 1, 1,

%e 1, 5, 1,

%e 1, 10, 10, 1,

%e 1, 16, 40, 16, 1,

%e 1, 23, 102, 102, 23, 1,

%e 1, 31, 209, 393, 209, 31, 1,

%e 1, 40, 376, 1122, 1122, 376, 40, 1,

%e 1, 50, 620, 2656, 4296, 2656, 620, 50, 1,

%e 1, 61, 960, 5536, 13100, 13100, 5536, 960, 61, 1,

%e 1, 73, 1417, 10522, 34036, 50180, 34036, 10522, 1417, 73, 1

%K nonn,easy,tabl

%O 0,5

%A _Paul Barry_, Apr 01 2011