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A099557 Slanted Pascal's triangle, read by rows, such that T(n,k) = binomial(n-[k/2],k) for [n*2/3]>=k>=0, where [x]=floor(x).

%I A099557 #3 Mar 30 2012 18:36:43
%S A099557 1,1,1,1,2,0,1,3,1,0,1,4,3,1,0,1,5,6,4,0,0,1,6,10,10,1,0,0,1,7,15,20,
%T A099557 5,1,0,0,1,8,21,35,15,6,0,0,0,1,9,28,56,35,21,1,0,0,0,1,10,36,84,70,
%U A099557 56,7,1,0,0,0,1,11,45,120,126,126,28,8,0,0,0,0
%N A099557 Slanted Pascal's triangle, read by rows, such that T(n,k) = binomial(n-[k/2],k) for [n*2/3]>=k>=0, where [x]=floor(x).
%C A099557 Row sums form A005314. Antidiagonal sums form A099558.
%F A099557 G.f.: (1-x+x*y)/((1-x)^2-x^3*y^2).
%e A099557 Rows begin:
%e A099557 [1],
%e A099557 [1,1],
%e A099557 [1,2,0],
%e A099557 [1,3,1,0],
%e A099557 [1,4,3,1,0],
%e A099557 [1,5,6,4,0,0],
%e A099557 [1,6,10,10,1,0,0],
%e A099557 [1,7,15,20,5,1,0,0],
%e A099557 [1,8,21,35,15,6,0,0,0],
%e A099557 [1,9,28,56,35,21,1,0,0,0],
%e A099557 [1,10,36,84,70,56,7,1,0,0,0],...
%e A099557 and can be derived from Pascal's triangle
%e A099557 by shifting each column k down by [k/2] rows.
%o A099557 (PARI) {T(n,k)=polcoeff(polcoeff((1-x+x*y)/((1-x)^2-x^3*y^2)+x*O(x^n),n,x)+y*O(y^k),k,y)}
%Y A099557 Cf. A005314, A099558.
%K A099557 nonn,tabl
%O A099557 0,5
%A A099557 _Paul D. Hanna_, Oct 22 2004