Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Apr 15 2022 13:02:59
%S 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 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 0,0,0,-9,-9,1,0,0,0,0,0,0,0,0,0,-10,-10,1
%N Matrix inverse of triangle A352650.
%F 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 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 Alt. row sums equal (-1)^n for n >= 0.
%F Matrix product with A094587 yields A097806.
%e The triangle T(n,k) for 0 <= k <= n starts:
%e n\k : 0 1 2 3 4 5 6 7 8 9
%e ======================================================
%e 0 : 1
%e 1 : 0 1
%e 2 : -1 -1 1
%e 3 : 0 -2 -2 1
%e 4 : 0 0 -3 -3 1
%e 5 : 0 0 0 -4 -4 1
%e 6 : 0 0 0 0 -5 -5 1
%e 7 : 0 0 0 0 0 -6 -6 1
%e 8 : 0 0 0 0 0 0 -7 -7 1
%e 9 : 0 0 0 0 0 0 0 -8 -8 1
%e etc.
%Y Cf. A094587, A097806, A352650.
%K sign,easy,tabl
%O 0,8
%A _Werner Schulte_, Apr 13 2022