%I
%S 1,1,1,1,2,1,1,4,3,1,1,8,8,4,1,1,16,21,13,5,1,1,32,55,41,19,6,1,1,64,
%T 144,129,69,26,7,1,1,128,377,406,250,106,34,8,1,1,256,987,1278,907,
%U 431,153,43,9,1,1,512,2584,4023,3292,1757,686,211,53,10,1,1,1024,6765,12664
%N Square array read by antidiagonals associated with sections of 1/(1xx^k).
%C Rows include A099242, A099253. Columns include A034856. Main diagonal is A099240. Sums of antidiagonals are A099241.
%F Square array T(n, k)=sum{j=0..n, binomial(k*n(k1)(j1), j)}, n, k>=0. Also, T(n, k)=sum{j=0..n, binomial(k+(n1)(j+1), n(j+1)1}, n>0. As a number triangle read by row, this is T(n, k)=sum{j=0..nk, binomial(k(nk)(k1)(j1)}. Rows of the square array are generated by 1/((1x)^kx). Rows satisfy a(n)=a(n1)sum{k=1..n, (1)^k^C(n, k)a(nk)}.
%e Rows begin
%e 1,1,1,1,1,1,1,...
%e 1,2,4,8,16,32,... 1section of 1/(1xx) A000079
%e 1,3,8,21,55,..... bisection of 1/(1xx^2) A001906
%e 1,4,13,41,129,... trisection of 1/(1xx^3) A052529 (essentially)
%e 1,5,19,69,250,... quadrisection of 1/(1xx^4) A055991
%e 1,6,26,106,431,.. quintisection of 1/(1xx^5) A079675 (essentially)
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Oct 08 2004
