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 A357883 #14 Oct 18 2022 13:31:38
%S A357883 1,1,0,1,1,0,1,0,2,0,1,0,1,6,0,1,0,0,3,24,0,1,0,0,1,14,120,0,1,0,0,0,
%T A357883 6,80,720,0,1,0,0,0,1,35,544,5040,0,1,0,0,0,0,10,235,4284,40320,0,1,0,
%U A357883 0,0,0,1,85,1834,38310,362880,0,1,0,0,0,0,0,15,735,16352,383256,3628800,0
%N A357883 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (k*j)!* |Stirling1(n,k*j)|/(k!^j * j!).
%F A357883 For k > 0, e.g.f. of column k: exp((-log(1-x))^k / k!).
%F A357883 T(0,k) = 1; T(n,k) = Sum_{j=1..n} binomial(n-1,j-1) * |Stirling1(j,k)| * T(n-j,k).
%e A357883 Square array begins:
%e A357883 1, 1, 1, 1, 1, 1, ...
%e A357883 0, 1, 0, 0, 0, 0, ...
%e A357883 0, 2, 1, 0, 0, 0, ...
%e A357883 0, 6, 3, 1, 0, 0, ...
%e A357883 0, 24, 14, 6, 1, 0, ...
%e A357883 0, 120, 80, 35, 10, 1, ...
%o A357883 (PARI) T(n, k) = sum(j=0, n, (k*j)!*abs(stirling(n, k*j, 1))/(k!^j*j!));
%o A357883 (PARI) T(n, k) = if(k==0, 0^n, n!*polcoef(exp((-log(1-x+x*O(x^n)))^k/k!), n));
%Y A357883 Columns k=0-5 give: A000007, A000142, A347001, A347002, A347003, A347004.
%Y A357883 Cf. A324162, A357119, A357881, A357882.
%K A357883 nonn,tabl
%O A357883 0,9
%A A357883 _Seiichi Manyama_, Oct 18 2022