This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A204040 #19 Feb 22 2013 14:40:24
%S A204040 1,0,1,0,2,1,0,0,4,1,0,-4,4,6,1,0,-4,-8,12,8,1,0,4,-24,-4,24,10,1,0,
%T A204040 12,-8,-60,16,40,12,1,0,4,56,-84,-96,60,60,14,1,0,-20,88,84,-272,-100,
%U A204040 136,84,16,1,0,-28,-40
%N A204040 Triangle T(n,k), read by rows, given by (0, 2, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C A204040 Antidiagonal sums : periodic sequence 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, ... (see A007877 or A098178).Riordan array (1, x*(1+x)/(1-x+2*x^2)) .
%F A204040 T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2, k-1) - 2*T(n-2,k).
%F A204040 G.f.: (1-x+2*x^2)/(1-(1+y)*x + (2-y)*x^2).
%F A204040 T(n,n) = n = A000012(n), T(n+1,n) = 2n = A005843(n), T(n+2,n) = A046092(n-1) for n>0, T(n+1,1) = A078050(n)*(-1)^n.
%F A204040 Sum_{k, 0<=k<=n} T(n,k) = A060747(n) = A005408(n-1).
%e A204040 Triangle begins :
%e A204040 1
%e A204040 0, 1
%e A204040 0, 2, 1
%e A204040 0, 0, 4, 1
%e A204040 0, -4, 4, 6, 1
%e A204040 0, -4, -8, 12, 8, 1
%e A204040 0, 4, -24, -4, 24, 10, 1
%e A204040 0, 12, -8, -60, 16, 40, 12, 1
%e A204040 0, 4, 56, -84, -96, 60, 60, 14, 1
%e A204040 0, -20, 88, 84, -272, -100, 136, 84, 16, 1
%Y A204040 Cf. A005408.
%K A204040 sign,tabl
%O A204040 0,5
%A A204040 _Philippe Deléham_, Jan 27 2012