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%I #9 Nov 27 2021 02:26:06
%S 1,-1,1,-2,0,1,0,-2,0,1,1,-2,-1,0,1,3,-1,-2,-1,0,1,4,0,-2,-1,-1,0,1,3,
%T 2,0,-2,-1,-1,0,1,3,3,0,-1,-1,-1,-1,0,1,0,4,2,0,-1,-1,-1,-1,0,1,0,4,2,
%U 1,-1,0,-1,-1,-1,0,1,-3,3,3,2,1,-1,0,-1,-1,-1,0,1,-4,3,3,2,1,0,0,0,-1,-1,-1,0,1
%N Matrix inverse of triangle A091602.
%H G. C. Greubel, <a href="/A091603/b091603.txt">Table of n, a(n) for n = 1..1275</a>
%e Triangle begins as:
%e 1;
%e -1, 1;
%e -2, 0, 1;
%e 0, -2, 0, 1;
%e 1, -2, -1, 0, 1;
%e 3, -1, -2, -1, 0, 1;
%e 4, 0, -2, -1, -1, 0, 1;
%e 3, 2, 0, -2, -1, -1, 0, 1;
%e 3, 3, 0, -1, -1, -1, -1, 0, 1;
%e 0, 4, 2, 0, -1, -1, -1, -1, 0, 1;
%e 0, 4, 2, 1, -1, 0, -1, -1, -1, 0, 1;
%e -3, 3, 3, 2, 1, -1, 0, -1, -1, -1, 0, 1;
%e -4, 3, 3, 2, 1, 0, 0, 0, -1, -1, -1, 0, 1;
%e -7, 2, 3, 2, 2, 1, 0, 0, 0, -1, -1, -1, 0, 1;
%e -9, 1, 3, 2, 2, 1, 0, 1, 0, 0, -1, -1, -1, 0, 1;
%t b[n_, i_, k_]:= b[n, i, k]= If[n==0, 1, If[i>n, 0, Sum[b[n-i*j, i+1, Min[k, Quotient[n-i*j, i+1]]], {j,0,k}]]];
%t t[n_, k_]:= t[n, k]= b[n, 1, k] - b[n, 1, k-1]; (* t = A091602 *)
%t M:= With[{p = 30}, Table[t[n, k], {n, p}, {k, p}]];
%t T:= Inverse[M];
%t Table[T[[n, k]], {n, 15}, {k, n}]//Flatten (* _G. C. Greubel_, Nov 26 2021 *)
%Y Cf. A091602, A091612 (column 1).
%K sign,tabl
%O 1,4
%A _Christian G. Bower_, Jan 23 2004
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