A387126 Triangle read by rows: T(n, k) = (n! / (n - k)!) * Product_{k=1..n} radical(k), where radical(n) is the product of distinct prime factors of n, cf. A007947.

1, 1, 1, 2, 4, 4, 6, 18, 36, 36, 12, 48, 144, 288, 288, 60, 300, 1200, 3600, 7200, 7200, 360, 2160, 10800, 43200, 129600, 259200, 259200, 2520, 17640, 105840, 529200, 2116800, 6350400, 12700800, 12700800, 5040, 40320, 282240, 1693440, 8467200, 33868800, 101606400, 203212800, 203212800

Offset: 0

Author

Peter Luschny, Aug 18 2025

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  [0]    1;
  [1]    1,     1;
  [2]    2,     4,      4;
  [3]    6,    18,     36,     36;
  [4]   12,    48,    144,    288,     288;
  [5]   60,   300,   1200,   3600,    7200,    7200;
  [6]  360,  2160,  10800,  43200,  129600,  259200,   259200;
  [7] 2520, 17640, 105840, 529200, 2116800, 6350400, 12700800, 12700800;
		

Crossrefs

Cf. A007947 (radical), A008279, A048803 (column 0), A277174 (main diagonal).

Programs

Maple

A387126 := (n, k) -> mul(NumberTheory:-Radical(j), j = 1..n) * n! / (n - k)!:

Mathematica

A387126[n_, k_] := Pochhammer[n-k+1, k] Times @@ ResourceFunction["IntegerRadical"][Range[1, n]];
Table[A387126[n, k], {n, 0, 8}, {k, 0, n}]  // Flatten

Formula

T(n, k) = A048803(n) * A008279(n, k).