%I #3 Mar 30 2012 18:59:13
%S 1,4,4,7,17,7,8,32,32,8,8,39,66,39,8,8,40,88,88,40,8,8,40,95,130,95,
%T 40,8,8,40,96,152,152,96,40,8,8,40,96,159,194,159,96,40,8,8,40,96,160,
%U 216,216,160,96,40,8,8,40,96,160,223,258,223,160,96,40,8
%N Correlation triangle for (1+x)^3/(1-x).
%C Row sums are A115293. Diagonal sums are A115294. T(2n,n) is A115295. T(2n,n)-T(2n,n+1) is 1,10,27,35,35,35,... The transform of (-1)^n by this matrix is 1,0,-3,0,4,0,-4,0,4,...
%F G.f.: (1+x)^3*(1+xy)^3/((1-x)(1-x*y)(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*A115291(k-j)*[j<=n-k]*A115291(n-k-j)}.
%e Triangle begins
%e 1;
%e 4, 4;
%e 7, 17, 7;
%e 8, 32, 32, 8;
%e 8, 39, 66, 39, 8;
%e 8, 40, 88, 88, 40, 8;
%e 8, 40, 95, 130, 95, 40, 8;
%e 8, 40, 96, 152, 152, 96, 40, 8;
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Jan 19 2006