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 A172250 #11 Jan 26 2020 01:05:16
%S A172250 1,0,1,0,1,0,0,0,2,-1,0,0,1,1,-1,0,0,0,3,-2,0,0,0,0,1,3,-4,1,0,0,0,0,
%T A172250 4,-2,-2,1,0,0,0,0,1,6,-9,3,0,0,0,0,0,0,5,0,-9,6,-1,0,0,0,0,0,1,10,
%U A172250 -15,3,3,-1,0,0,0,0,0,0,6,5,-24,18,-4,0,0,0,0,0,0,0,1,15,-20,-6,18,-8,1
%N A172250 Triangle, read by rows, given by [0,1,-1,0,0,0,0,0,0,0,...] DELTA [1,-1,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
%F A172250 T(n,k) = T(n-1,k-1) + T(n-2,k-1) - T(n-2,k-2), T(0,0)=1, T(n,k) = 0 if k > n or if k < 0.
%F A172250 Sum_{k=0..n} T(n,k)*x^k = (-1)^n*A088139(n+1), A001607(n+1), A000007(n), A000012(n), A099087(n), A190960(n+1) for x = -2, -1, 0, 1, 2, 3 respectively. - _Philippe Deléham_, Feb 15 2012
%F A172250 G.f.: 1/(1-y*x+y*(y-1)*x^2). - _Philippe Deléham_, Feb 15 2012
%e A172250 Triangle begins:
%e A172250 1;
%e A172250 0, 1;
%e A172250 0, 1, 0;
%e A172250 0, 0, 2, -1;
%e A172250 0, 0, 1, 1, -1;
%e A172250 0, 0, 0, 3, -2, 0;
%e A172250 0, 0, 0, 1, 3, -4, 1;
%e A172250 0, 0, 0, 0, 4, -2, -2, 1; ...
%Y A172250 Cf. A101950.
%K A172250 sign,tabl
%O A172250 0,9
%A A172250 _Philippe Deléham_, Jan 29 2010