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 A362837 #17 May 05 2023 12:23:54
%S A362837 1,1,0,1,0,0,1,0,2,0,1,0,4,3,0,1,0,6,12,20,0,1,0,8,27,112,90,0,1,0,10,
%T A362837 48,324,960,594,0,1,0,12,75,704,4050,10848,4200,0,1,0,14,108,1300,
%U A362837 11520,64962,141120,34544,0,1,0,16,147,2160,26250,239616,1224720,2122496,316008,0
%N A362837 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = (-1)^n * n! * Sum_{j=0..floor(n/2)} k^(n-j) * Stirling1(n-j,j)/(n-j)!.
%F A362837 E.g.f. of column k: 1/(1 - k * x)^x.
%e A362837 Square array begins:
%e A362837 1, 1, 1, 1, 1, 1, ...
%e A362837 0, 0, 0, 0, 0, 0, ...
%e A362837 0, 2, 4, 6, 8, 10, ...
%e A362837 0, 3, 12, 27, 48, 75, ...
%e A362837 0, 20, 112, 324, 704, 1300, ...
%e A362837 0, 90, 960, 4050, 11520, 26250, ...
%o A362837 (PARI) T(n, k) = (-1)^n*n!*sum(j=0, n\2, k^(n-j)*stirling(n-j, j, 1)/(n-j)!);
%Y A362837 Columns k=0..3 give: A000007, A066166, A053491, A351735.
%Y A362837 Main diagonal gives A362838.
%Y A362837 Cf. A362834.
%K A362837 nonn,tabl
%O A362837 0,9
%A A362837 _Seiichi Manyama_, May 05 2023