A104731 - OEIS

%I #5 Sep 17 2013 13:21:28

%S 1,1,2,1,5,3,1,5,11,4,1,5,16,19,5,1,5,16,37,29,6,1,5,16,44,71,41,7,1,

%T 5,16,44,103,121,55,8,1,5,16,44,112,211,190,71,9,1,5,16,44,112,261,

%U 390,281,89,10,1,5,16,44,112,272,555,666,397,109,11

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

%F Product of the triangles A(n,k) = k+1 and B = binomial(k,n-k) = [1; 0, 1; 0, 1, 1; 0, 0, 2, 1; 0, 0, 1, 3, 1;...], the triangular view of A026729.

%e The first few rows of the triangle are:

%e 1;

%e 1, 2;

%e 1, 5, 3;

%e 1, 5, 11, 4

%e 1, 5, 16, 19, 5;

%e 1, 5, 16, 37, 29, 6;

%e ...

%Y Cf. A014286 (row sums), A045925, A026729.

%K nonn,tabl

%O 0,3

%A _Gary W. Adamson_, Mar 20 2005