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 A291980 #13 May 12 2024 10:05:17
%S A291980 1,1,1,1,2,1,2,3,3,1,4,8,6,4,1,14,20,20,10,5,1,38,84,60,40,15,6,1,216,
%T A291980 266,294,140,70,21,7,1,600,1728,1064,784,280,112,28,8,1,6240,5400,
%U A291980 7776,3192,1764,504,168,36,9,1
%N A291980 Triangle read by rows, T(n, k) = n!*[t^k] ([x^n] exp(x*t)/(1 - log(1+x))) for 0<=k<=n.
%F A291980 T(n, k) = binomial(n, n - k)*Sum_{j=0..n - k} j!*Stirling1(n - k, j). - _Detlef Meya_, May 12 2024
%e A291980 Triangle starts:
%e A291980 [1]
%e A291980 [1, 1]
%e A291980 [1, 2, 1]
%e A291980 [2, 3, 3, 1]
%e A291980 [4, 8, 6, 4, 1]
%e A291980 [14, 20, 20, 10, 5, 1]
%e A291980 [38, 84, 60, 40, 15, 6, 1]
%e A291980 [216, 266, 294, 140, 70, 21, 7, 1]
%e A291980 [600, 1728, 1064, 784, 280, 112, 28, 8, 1]
%p A291980 T_row := proc(n) exp(x*t)/(1 - log(1+x)): series(%, x, n+1):
%p A291980 seq(n!*coeff(coeff(%,x,n), t, k), k=0..n) end:
%p A291980 seq(T_row(n), n=0..10);
%t A291980 T[n_, k_] := Binomial[n, n - k]*Sum[j!*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 A291980 Row sums: A291981.
%Y A291980 Columns: A006252 (c=1), A108125 (c=2).
%Y A291980 Diagonals: A000217 (d=3), A007290 (d=4), A033488 (d=5).
%Y A291980 Cf. A291978.
%K A291980 nonn,tabl
%O A291980 0,5
%A A291980 _Peter Luschny_, Sep 15 2017