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 A124645 #11 May 01 2021 22:03:07
%S A124645 1,1,-1,0,1,-1,0,1,-2,1,0,0,1,-2,1,0,0,1,-3,3,-1,0,0,0,1,-3,3,-1,0,0,
%T A124645 0,1,-4,6,-4,1,0,0,0,0,1,-4,6,-4,1,0,0,0,0,1,-5,10,-10,5,-1,0,0,0,0,0,
%U A124645 1,-5,10,-10,5,-1,0,0,0,0,0,1,-6,15,-20,15,-6,1,0,0,0,0,0,0,1,-6,15,-20,15,-6,1
%N A124645 Triangle T(n,k), 0<=k<=n, read by rows given by [1,-1,0,0,0,0,0,...] DELTA [ -1,2,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 .
%C A124645 Matrix inverse of A108299.
%H A124645 G. C. Greubel, <a href="/A124645/b124645.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A124645 Row n has g.f.: x^[n/2]*(1-x)^(n-[n/2]).
%F A124645 G.f.: (1-x*y+x)/(1-x^2*y+x^2*y^2). - _R. J. Mathar_, Aug 11 2015
%F A124645 T(n, k) = (-1)^(k + floor(n/2)) * binomial(floor((n+1)/2), k - floor(n/2)). - _G. C. Greubel_, May 01 2021
%e A124645 Triangle begins:
%e A124645 1;
%e A124645 1, -1;
%e A124645 0, 1, -1;
%e A124645 0, 1, -2, 1;
%e A124645 0, 0, 1, -2, 1;
%e A124645 0, 0, 1, -3, 3, -1;
%e A124645 0, 0, 0, 1, -3, 3, -1;
%e A124645 0, 0, 0, 1, -4, 6, -4, 1;
%e A124645 0, 0, 0, 0, 1, -4, 6, -4, 1;
%e A124645 0, 0, 0, 0, 1, -5, 10, -10, 5, -1;
%e A124645 0, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1;
%e A124645 0, 0, 0, 0, 0, 1, -6, 15, -20, 15, -6, 1;
%t A124645 Table[(-1)^(Floor[n/2]+k)*Binomial[Floor[(n+1)/2], k-Floor[n/2]], {n, 0, 12}, {k, 0, n}]//Flatten (* _G. C. Greubel_, May 01 2021 *)
%o A124645 (Magma) [(-1)^(k+Floor(n/2))*Binomial(Floor((n+1)/2), k-Floor(n/2)): k in [0..n], n in [0..12]]; // _G. C. Greubel_, May 01 2021
%o A124645 (Sage) flatten([[(-1)^(k+(n//2))*binomial(((n+1)//2), k-(n//2)) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, May 01 2021
%K A124645 sign,tabl
%O A124645 0,9
%A A124645 _Philippe Deléham_, Jun 13 2007, Aug 22 2007