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 A352988 #7 Apr 15 2022 13:02:59
%S A352988 1,0,1,-1,-1,1,0,-2,-2,1,0,0,-3,-3,1,0,0,0,-4,-4,1,0,0,0,0,-5,-5,1,0,
%T A352988 0,0,0,0,-6,-6,1,0,0,0,0,0,0,-7,-7,1,0,0,0,0,0,0,0,-8,-8,1,0,0,0,0,0,
%U A352988 0,0,0,-9,-9,1,0,0,0,0,0,0,0,0,0,-10,-10,1
%N A352988 Matrix inverse of triangle A352650.
%F A352988 T(n,n) = 1 for n >= 0, and T(n,n-1) = 1 - n for n > 0, and T(n,n-2) = 1 - n for n > 1, and T(n,k) = 0 if n < 0 or k < 0 or n < k or n > k+2.
%F A352988 G.f.: Sum_{n>=0, k=0..n} T(n,k) * x^k * t^n = (1 + t) * (1 - (1 + x) * t) / (1 - x * t)^2.
%F A352988 Alt. row sums equal (-1)^n for n >= 0.
%F A352988 Matrix product with A094587 yields A097806.
%e A352988 The triangle T(n,k) for 0 <= k <= n starts:
%e A352988 n\k : 0 1 2 3 4 5 6 7 8 9
%e A352988 ======================================================
%e A352988 0 : 1
%e A352988 1 : 0 1
%e A352988 2 : -1 -1 1
%e A352988 3 : 0 -2 -2 1
%e A352988 4 : 0 0 -3 -3 1
%e A352988 5 : 0 0 0 -4 -4 1
%e A352988 6 : 0 0 0 0 -5 -5 1
%e A352988 7 : 0 0 0 0 0 -6 -6 1
%e A352988 8 : 0 0 0 0 0 0 -7 -7 1
%e A352988 9 : 0 0 0 0 0 0 0 -8 -8 1
%e A352988 etc.
%Y A352988 Cf. A094587, A097806, A352650.
%K A352988 sign,easy,tabl
%O A352988 0,8
%A A352988 _Werner Schulte_, Apr 13 2022