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 A362834 #21 May 05 2023 12:24:37
%S A362834 1,1,0,1,0,0,1,0,2,0,1,0,4,3,0,1,0,6,6,20,0,1,0,8,9,64,90,0,1,0,10,12,
%T A362834 132,300,594,0,1,0,12,15,224,630,2568,4200,0,1,0,14,18,340,1080,6642,
%U A362834 20160,34544,0,1,0,16,21,480,1650,13536,55440,193856,316008,0
%N A362834 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^j * Stirling1(n-j,j)/(n-j)!.
%F A362834 E.g.f. of column k: 1/(1 - x)^(k*x).
%e A362834 Square array begins:
%e A362834 1, 1, 1, 1, 1, 1, ...
%e A362834 0, 0, 0, 0, 0, 0, ...
%e A362834 0, 2, 4, 6, 8, 10, ...
%e A362834 0, 3, 6, 9, 12, 15, ...
%e A362834 0, 20, 64, 132, 224, 340, ...
%e A362834 0, 90, 300, 630, 1080, 1650, ...
%o A362834 (PARI) T(n, k) = (-1)^n*n!*sum(j=0, n\2, k^j*stirling(n-j, j, 1)/(n-j)!);
%Y A362834 Columns k=0..3 give: A000007, A066166, A053489, A053490.
%Y A362834 Main diagonal gives A318615.
%Y A362834 Cf. A361652.
%K A362834 nonn,tabl
%O A362834 0,9
%A A362834 _Seiichi Manyama_, May 05 2023