|
%I #15 Nov 12 2021 12:24:05
%S 1,-2,1,-5,2,1,-2,0,0,1,4,-2,0,-2,1,10,-4,-2,-5,2,1,-5,0,0,2,0,0,1,10,
%T -5,0,-4,2,0,-2,1,25,-10,-5,-10,4,2,-5,2,1,-2,0,0,0,0,0,0,0,0,1,4,-2,
%U 0,0,0,0,0,0,0,-2,1,10,-4,-2,0,0,0,0,0,0,-5,2,1,4,0,0,-2,0,0,0,0,0,-2,0,0,1,-8,4,0,4,-2,0,0,0,0,4,-2,0,-2,1
%N Inverse of number triangle A117939.
%C Row sums are A117942.
%C T(n, k) mod 2 = A117944(n,k).
%H G. C. Greubel, <a href="/A117941/b117941.txt">Rows n = 0..50 of the triangle, flattened</a>
%e Triangle begins
%e 1;
%e -2, 1;
%e -5, 2, 1;
%e -2, 0, 0, 1;
%e 4, -2, 0, -2, 1;
%e 10, -4, -2, -5, 2, 1;
%e -5, 0, 0, 2, 0, 0, 1;
%e 10, -5, 0, -4, 2, 0, -2, 1;
%e 25, -10, -5, -10, 4, 2, -5, 2, 1;
%t M[n_, k_]:= M[n, k]= If[k>n, 0, Sum[JacobiSymbol[Binomial[n, j], 3]*JacobiSymbol[Binomial[n-j, k], 3], {j,0,n}], 0];
%t m:= m= With[{q = 60}, Table[M[n, k], {n,0,q}, {k,0,q}]];
%t T[n_, k_]:= Inverse[m][[n+1, k+1]];
%t Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Oct 29 2021 *)
%Y Cf. A117939, A117942, A117944.
%K sign,tabl
%O 0,2
%A _Paul Barry_, Apr 05 2006
|
