%I #14 Jul 22 2022 10:36:21
%S 1,1,1,1,3,1,1,6,4,1,1,30,20,5,1,1,60,60,30,6,1,1,420,420,210,42,7,1,
%T 1,840,3360,840,336,56,8,1,1,7560,10080,7560,3024,504,72,9,1,1,15120,
%U 100800,75600,15120,5040,720,90,10,1,1,166320,1108800,831600,166320,55440,7920,990,110,11,1
%N Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) = n!/(k! * floor(n/k)!).
%F E.g.f. of column k: (1 - x^k) * (exp(x^k) - 1)/(k! * (1 - x)).
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 3, 1;
%e 1, 6, 4, 1;
%e 1, 30, 20, 5, 1;
%e 1, 60, 60, 30, 6, 1;
%e 1, 420, 420, 210, 42, 7, 1;
%e 1, 840, 3360, 840, 336, 56, 8, 1;
%e ...
%t T[n_, k_] := n!/(k!*Floor[n/k]!); Table[T[n, k], {n, 1, 11}, {k, 1, n}] // Flatten (* _Amiram Eldar_, Jul 22 2022 *)
%o (PARI) T(n, k) = n!/(k!*(n\k)!);
%Y Row sums give A355991.
%Y Column k=1..3 give A000012, A355989, A355990.
%K nonn,tabl
%O 1,5
%A _Seiichi Manyama_, Jul 22 2022