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 A291978 #16 May 12 2024 10:05:00
%S A291978 1,1,1,3,2,1,14,9,3,1,88,56,18,4,1,694,440,140,30,5,1,6578,4164,1320,
%T A291978 280,45,6,1,72792,46046,14574,3080,490,63,7,1,920904,582336,184184,
%U A291978 38864,6160,784,84,8,1,13109088,8288136,2620512,552552,87444,11088,1176,108,9,1
%N A291978 Triangle read by rows, T(n, k) = (-1)^(n-k)*n!*[t^k]([x^n] exp(x*t)/(1 + log(1+x))) for 0<=k<=n.
%F A291978 T(n, k) = binomial(n, n - k)*Sum_{j=0..n - k} j!*abs(Stirling1(n - k, j)). - _Detlef Meya_, May 12 2024
%e A291978 Triangle starts:
%e A291978 [1]
%e A291978 [1, 1]
%e A291978 [3, 2, 1]
%e A291978 [14, 9, 3, 1]
%e A291978 [88, 56, 18, 4, 1]
%e A291978 [694, 440, 140, 30, 5, 1]
%e A291978 [6578, 4164, 1320, 280, 45, 6, 1]
%e A291978 [72792, 46046, 14574, 3080, 490, 63, 7, 1]
%e A291978 [920904, 582336, 184184, 38864, 6160, 784, 84, 8, 1]
%p A291978 T_row := proc(n) exp(x*t)/(1 + log(1+x)): series(%, x, n+1):
%p A291978 seq(coeff((-1)^(n-k)*n!*coeff(%,x,n),t,k), k=0..n) end:
%p A291978 seq(T_row(n), n=0..9);
%t A291978 T[n_, k_] := Binomial[n, n - k]*Sum[j!*Abs[StirlingS1[n - k, j]], {j, 0, n - k}]; Flatten[Table[T[n, k], {n, 0, 9}, {k, 0, n}]] (* _Detlef Meya_, May 12 2024 *)
%Y A291978 Row sums: A291978.
%Y A291978 Columns: A007840 (c=1), A052860 (c=2).
%Y A291978 Diagonal: A045943 (d=3).
%Y A291978 Cf. A291980.
%K A291978 nonn,tabl
%O A291978 0,4
%A A291978 _Peter Luschny_, Sep 15 2017