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 A367824 #24 Dec 08 2023 11:38:50
%S A367824 1,1,-1,1,0,-1,1,1,-1,-1,1,1,0,-1,-1,1,3,1,-1,-3,-1,1,2,1,0,-1,-2,-1,
%T A367824 1,5,3,1,-1,-3,-5,-1,1,3,1,1,0,-1,-1,-3,-1,1,7,5,1,1,-1,-1,-5,-7,-1,1,
%U A367824 4,3,2,1,0,-1,-2,-3,-4,-1,1,0,7,5,3,1,-1,-3,-5,-7,-9,-1
%N A367824 Array read by ascending antidiagonals: A(n, k) is the numerator of (R(n) - k)/(n + k), where R(n) is the digit reversal of n, with A(0, 0) = 1.
%C A367824 This array generalizes A367727.
%H A367824 Stefano Spezia, <a href="/A367824/b367824.txt">First 151 antidiagonals of the array</a>
%F A367824 A(1, n) = -A026741(n-1) for n > 0.
%F A367824 A(2, n) = -A060819(n-2) for n > 2.
%F A367824 A(3, n) = -A060789(n-3) for n > 3.
%F A367824 A(4, n) = -A106609(n-4) for n > 3.
%F A367824 A(5, n) = -A106611(n-5) for n > 4.
%F A367824 A(6, n) = -A051724(n-6) for n > 5.
%F A367824 A(7, n) = -A106615(n-7) for n > 6.
%F A367824 A(8, n) = -A106617(n-8) = A231190(n) for n > 7.
%F A367824 A(9, n) = -A106619(n-9) for n > 8.
%F A367824 A(10, n) = -A106612(n-10) for n > 9.
%e A367824 The array of the fractions begins:
%e A367824 1, -1, -1, -1, -1, -1, -1, -1, ...
%e A367824 1, 0, -1/3, -1/2, -3/5, -2/3, -5/7, -3/4, ...
%e A367824 1, 1/3, 0, -1/5, -1/3, -3/7, -1/2, -5/9, ...
%e A367824 1, 1/2, 1/5, 0, -1/7, -1/4, -1/3, -2/5, ...
%e A367824 1, 3/5, 1/3, 1/7, 0, -1/9, -1/5, -3/11, ...
%e A367824 1, 2/3, 3/7, 1/4, 1/9, 0, -1/11, -1/6, ...
%e A367824 1, 5/7, 1/2, 1/3, 1/5, 1/11, 0, -1/13, ...
%e A367824 1, 3/4, 5/9, 2/5, 3/11, 1/6, 1/13, 0, ...
%e A367824 ...
%e A367824 The array of the numerators begins:
%e A367824 1, -1, -1, -1, -1, -1, -1, -1, ...
%e A367824 1, 0, -1, -1, -3, -2, -5, -3, ...
%e A367824 1, 1, 0, -1, -1, -3, -1, -5, ...
%e A367824 1, 1, 1, 0, -1, -1, -1, -2, ...
%e A367824 1, 3, 1, 1, 0, -1, -1, -3, ...
%e A367824 1, 2, 3, 1, 1, 0, -1, -1, ...
%e A367824 1, 5, 1, 1, 1, 1, 0, -1, ...
%e A367824 1, 3, 5, 2, 3, 1, 1, 0, ...
%e A367824 ...
%t A367824 A[0,0]=1; A[n_,k_]:=Numerator[(FromDigits[Reverse[IntegerDigits[n]]]-k)/(n+k)]; Table[A[n-k,k],{n,0,11},{k,0,n}]//Flatten
%Y A367824 Cf. A367825 (denominator), A367826 (antidiagonal sums).
%Y A367824 Cf. A004086, A026741, A051724, A060789, A060819, A106609, A106611, A106612, A106617, A106619, A153881 (n=0), A231190, A367727 (k=1).
%K A367824 sign,base,frac,look,tabl
%O A367824 0,17
%A A367824 _Stefano Spezia_, Dec 02 2023