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 A361652 #30 May 05 2023 12:25:05
%S A361652 1,1,0,1,0,0,1,0,2,0,1,0,4,3,0,1,0,6,6,16,0,1,0,8,9,56,65,0,1,0,10,12,
%T A361652 120,250,336,0,1,0,12,15,208,555,1812,1897,0,1,0,14,18,320,980,5148,
%U A361652 12614,11824,0,1,0,16,21,456,1525,11064,39711,101040,80145,0
%N A361652 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/2)} k^j * Stirling2(n-j,j)/(n-j)!.
%F A361652 E.g.f. of column k: exp(k * x * (exp(x) - 1)).
%e A361652 Square array begins:
%e A361652 1, 1, 1, 1, 1, 1, ...
%e A361652 0, 0, 0, 0, 0, 0, ...
%e A361652 0, 2, 4, 6, 8, 10, ...
%e A361652 0, 3, 6, 9, 12, 15, ...
%e A361652 0, 16, 56, 120, 208, 320, ...
%e A361652 0, 65, 250, 555, 980, 1525, ...
%o A361652 (PARI) T(n, k) = n!*sum(j=0, n\2, k^j*stirling(n-j, j, 2)/(n-j)!);
%Y A361652 Columns k=0..3 give: A000007, A052506, A351733, A351734.
%Y A361652 Main diagonal gives (-1)^n * A290158(n).
%Y A361652 Cf. A362834.
%K A361652 nonn,tabl
%O A361652 0,9
%A A361652 _Seiichi Manyama_, May 05 2023