|
%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
|
