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A117941 Inverse of number triangle A117939.

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