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 A221179 #14 Feb 22 2013 14:40:40
%S A221179 1,0,1,0,1,1,0,0,2,1,0,-2,1,3,1,0,-4,-4,3,4,1,0,-4,-12,-5,6,5,1,0,0,
%T A221179 -16,-24,-4,10,6,1,0,8,-4,-42,-39,0,15,7,1,0,16,32,-24,-88,-55,8,21,8,
%U A221179 1,0,16,80,72,-80
%N A221179 A convolution triangle of numbers obtained from A146559.
%C A221179 Triangle T(n,k) given by (0, 1, -1, 2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%F A221179 G.f. for the k-th column: ((x-x^2)/(1-2*x+2*x^2))^k.
%F A221179 G.f.: (1-2*x+2*x^2)/(1-2*x+2*x^2-x*y+x^2*y).
%F A221179 T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k) - T(n-2,k-1), T(0,0)=1, T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.
%F A221179 T(n,k) = (-1)^(n-k)*A181472(n-1,k-1) for n>0 and k>0.
%F A221179 T(n,1) = A146559(n-1).
%F A221179 T(n+1,n) = n = A001477(n).
%F A221179 T(n+2,n) = (n^2-n)/2 = A161680(n).
%F A221179 Sum_{k, 0<=k<=n} T(n,k) = A057682(n) for n>0.
%e A221179 Triangle begins:
%e A221179 1
%e A221179 0, 1
%e A221179 0, 1, 1
%e A221179 0, 0, 2, 1
%e A221179 0, -2, 1, 3, 1
%e A221179 0, -4, -4, 3, 4, 1
%e A221179 0, -4, -12, -5, 6, 5, 1
%e A221179 0, 0, -16, -24, -4, 10, 6, 1
%Y A221179 Cf. A030523, A104597, A181472, A220399
%K A221179 sign,tabl
%O A221179 0,9
%A A221179 _Philippe Deléham_, Feb 20 2013