This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091603 #9 Nov 27 2021 02:26:06 %S A091603 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 A091603 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 A091603 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 A091603 Matrix inverse of triangle A091602. %H A091603 G. C. Greubel, <a href="/A091603/b091603.txt">Table of n, a(n) for n = 1..1275</a> %e A091603 Triangle begins as: %e A091603 1; %e A091603 -1, 1; %e A091603 -2, 0, 1; %e A091603 0, -2, 0, 1; %e A091603 1, -2, -1, 0, 1; %e A091603 3, -1, -2, -1, 0, 1; %e A091603 4, 0, -2, -1, -1, 0, 1; %e A091603 3, 2, 0, -2, -1, -1, 0, 1; %e A091603 3, 3, 0, -1, -1, -1, -1, 0, 1; %e A091603 0, 4, 2, 0, -1, -1, -1, -1, 0, 1; %e A091603 0, 4, 2, 1, -1, 0, -1, -1, -1, 0, 1; %e A091603 -3, 3, 3, 2, 1, -1, 0, -1, -1, -1, 0, 1; %e A091603 -4, 3, 3, 2, 1, 0, 0, 0, -1, -1, -1, 0, 1; %e A091603 -7, 2, 3, 2, 2, 1, 0, 0, 0, -1, -1, -1, 0, 1; %e A091603 -9, 1, 3, 2, 2, 1, 0, 1, 0, 0, -1, -1, -1, 0, 1; %t A091603 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 A091603 t[n_, k_]:= t[n, k]= b[n, 1, k] - b[n, 1, k-1]; (* t = A091602 *) %t A091603 M:= With[{p = 30}, Table[t[n, k], {n, p}, {k, p}]]; %t A091603 T:= Inverse[M]; %t A091603 Table[T[[n, k]], {n, 15}, {k, n}]//Flatten (* _G. C. Greubel_, Nov 26 2021 *) %Y A091603 Cf. A091602, A091612 (column 1). %K A091603 sign,tabl %O A091603 1,4 %A A091603 _Christian G. Bower_, Jan 23 2004