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 A320079 #18 Sep 10 2023 10:18:43
%S A320079 1,1,0,1,1,0,1,2,3,0,1,3,10,14,0,1,4,21,76,88,0,1,5,36,222,772,694,0,
%T A320079 1,6,55,488,3132,9808,6578,0,1,7,78,910,8824,55242,149552,72792,0,1,8,
%U A320079 105,1524,20080,199456,1169262,2660544,920904,0,1,9,136,2366,39708,553870,5410208,28873800,54093696,13109088,0
%N A320079 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 + k*log(1 - x)).
%F A320079 E.g.f. of column k: 1/(1 + k*log(1 - x)).
%F A320079 A(n,k) = Sum_{j=0..n} |Stirling1(n,j)|*j!*k^j.
%F A320079 A(0,k) = 1; A(n,k) = k * Sum_{j=1..n} (j-1)! * binomial(n,j) * A(n-j,k). - _Seiichi Manyama_, May 22 2022
%e A320079 E.g.f. of column k: A_k(x) = 1 + k*x/1! + k*(2*k + 1)*x^2/2! + 2*k*(3*k^2 + 3*k + 1)*x^3/3! + 2*k*(12*k^3 + 18*k^2 + 11*k + 3)*x^4/4! + ...
%e A320079 Square array begins:
%e A320079 1, 1, 1, 1, 1, 1, ...
%e A320079 0, 1, 2, 3, 4, 5, ...
%e A320079 0, 3, 10, 21, 36, 55, ...
%e A320079 0, 14, 76, 222, 488, 910, ...
%e A320079 0, 88, 772, 3132, 8824, 20080, ...
%e A320079 0, 694, 9808, 55242, 199456, 553870, ...
%t A320079 Table[Function[k, n! SeriesCoefficient[1/(1 + k Log[1 - x]), {x, 0, n}]][j - n], {j, 0, 10}, {n, 0, j}] // Flatten
%Y A320079 Columns k=0..5 give A000007, A007840, A088500, A354263, A354264, A365588.
%Y A320079 Main diagonal gives A317171.
%Y A320079 Cf. A048594, A048994, A094416, A320080.
%K A320079 nonn,tabl
%O A320079 0,8
%A A320079 _Ilya Gutkovskiy_, Oct 05 2018