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%I #6 Mar 15 2021 21:30:33
%S 1,0,1,0,1,1,0,1,1,1,0,3,2,1,1,0,4,3,2,1,1,0,10,7,4,2,1,1,0,18,13,7,4,
%T 2,1,1,0,37,26,15,8,4,2,1,1,0,71,51,29,15,8,4,2,1,1,0,146,104,59,31,
%U 16,8,4,2,1,1,0,285,203,115,61,31,16,8,4,2,1,1,0,577,411,233,123,63,32,16,8,4,2,1,1
%N Matrix inverse of A155031.
%H G. C. Greubel, <a href="/A155033/b155033.txt">Rows n = 1..50 of the triangle, flattened</a>
%F Sum_{k=1..n} T(n,k) = A101173(n). - _G. C. Greubel_, Mar 15 2021
%e Table begins and row sums are:
%e 1 = 1;
%e 0, 1 = 1;
%e 0, 1, 1 = 2;
%e 0, 1, 1, 1 = 3;
%e 0, 3, 2, 1, 1 = 7;
%e 0, 4, 3, 2, 1, 1 = 11;
%e 0, 10, 7, 4, 2, 1, 1 = 25;
%e 0, 18, 13, 7, 4, 2, 1, 1 = 46;
%e 0, 37, 26, 15, 8, 4, 2, 1, 1 = 94;
%t A155031[n_, k_]:= If[k>n, 0, If[k==n, 1, If[k==1 || Mod[n, k]==0, 0, -1]]];
%t A155033:= Inverse[Table[A155031[n, k], {n,30}, {k,30}]];
%t Table[A155033[[n, k]], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Mar 15 2021 *)
%Y Cf. A101173.
%K nonn,tabl
%O 1,12
%A _Mats Granvik_, Jan 19 2009
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