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 A196389 #21 Jan 26 2020 01:01:50
%S A196389 1,0,1,0,1,1,0,0,2,1,0,0,0,3,1,0,0,0,0,4,1,0,0,0,0,0,5,1,0,0,0,0,0,0,
%T A196389 6,1,0,0,0,0,0,0,0,7,1,0,0,0,0,0,0,0,0,8,1,0,0,0,0,0,0,0,0,0,9,1
%N A196389 Triangle T(n,k), read by rows, given by (0,1,-1,0,0,0,0,0,0,0,...) DELTA (1,0,0,1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.
%C A196389 Row sums are A028310; diagonal sums are A057979; column sums are A000027.
%F A196389 T(n,n)=1, T(n+1,n)=n.
%F A196389 G.f.: (1-x*y+x^2*y)/(1-x*y)^2. - _Philippe Deléham_, Oct 31 2011
%F A196389 Sum_{k=0..n} T(n,k)*x^k = A000007(n), A028310(n), A057711(n+1), A064017(n+1) for x = 0, 1, 2, 3 respectively. - _Philippe Deléham_, Oct 31 2011
%e A196389 Triangle begins:
%e A196389 1;
%e A196389 0, 1;
%e A196389 0, 1, 1;
%e A196389 0, 0, 2, 1;
%e A196389 0, 0, 0, 3, 1;
%e A196389 0, 0, 0, 0, 4, 1;
%e A196389 0, 0, 0, 0, 0, 5, 1;
%e A196389 0, 0, 0, 0, 0, 0, 6, 1;
%e A196389 0, 0, 0, 0, 0, 0, 0, 7, 1;
%e A196389 0, 0, 0, 0, 0, 0, 0, 0, 8, 1;
%e A196389 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1; ...
%Y A196389 Cf. A084938.
%K A196389 nonn,tabl,easy
%O A196389 0,9
%A A196389 _Philippe Deléham_, Oct 28 2011