A355996 Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) = n!/(k! * floor(n/k)!).

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, 1, 840, 3360, 840, 336, 56, 8, 1, 1, 7560, 10080, 7560, 3024, 504, 72, 9, 1, 1, 15120, 100800, 75600, 15120, 5040, 720, 90, 10, 1, 1, 166320, 1108800, 831600, 166320, 55440, 7920, 990, 110, 11, 1

Offset: 1

Author

Seiichi Manyama, Jul 22 2022

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  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;
  1, 840, 3360, 840, 336, 56, 8, 1;
  ...
		

Crossrefs

Row sums give A355991.

Column k=1..3 give A000012, A355989, A355990.

Programs

Mathematica

T[n_, k_] := n!/(k!*Floor[n/k]!); Table[T[n, k], {n, 1, 11}, {k, 1, n}] // Flatten (* Amiram Eldar, Jul 22 2022 *)

PARI

T(n, k) = n!/(k!*(n\k)!);

Formula

E.g.f. of column k: (1 - x^k) * (exp(x^k) - 1)/(k! * (1 - x)).