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 A334192 #5 Apr 18 2020 11:49:55
%S A334192 1,1,0,1,0,-1,1,0,-2,-1,1,0,-3,-4,2,1,0,-4,-9,4,9,1,0,-5,-16,0,64,9,1,
%T A334192 0,-6,-25,-16,189,248,-50,1,0,-7,-36,-50,384,1377,48,-267,1,0,-8,-49,
%U A334192 -108,625,4416,4374,-6512,-413,1,0,-9,-64,-196,864,10625,26368,-26001,-51200,2180
%N A334192 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = exp(1/k) * Sum_{j>=0} (k*j + 1)^n / ((-k)^j * j!).
%F A334192 G.f. of column k: (1/(1 - x)) * Sum_{j>=0} (-x/(1 - x))^j / Product_{i=1..j} (1 - k*i*x/(1 - x)).
%F A334192 E.g.f. of column k: exp(x + (1 - exp(k*x)) / k).
%e A334192 Square array begins:
%e A334192 1, 1, 1, 1, 1, 1, ...
%e A334192 0, 0, 0, 0, 0, 0, ...
%e A334192 -1, -2, -3, -4, -5, -6, ...
%e A334192 -1, -4, -9, -16, -25, -36, ...
%e A334192 2, 4, 0, -16, -50, -108, ...
%e A334192 9, 64, 189, 384, 625, 864, ...
%t A334192 Table[Function[k, SeriesCoefficient[1/(1 - x) Sum[(-x/(1 - x))^j/Product[(1 - k i x/(1 - x)), {i, 1, j}], {j, 0, n}], {x, 0, n}]][m - n + 1], {m, 0, 10}, {n, 0, m}] // Flatten
%t A334192 Table[Function[k, n! SeriesCoefficient[Exp[x + (1 - Exp[k x])/k], {x, 0, n}]][m - n + 1], {m, 0, 10}, {n, 0, m}] // Flatten
%Y A334192 Columns k=1..3 give A293037, A334190, A334191.
%Y A334192 Cf. A309386, A334165, A334193 (diagonal).
%K A334192 sign,tabl
%O A334192 0,9
%A A334192 _Ilya Gutkovskiy_, Apr 18 2020