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

0,4

Links

Table of n, a(n) for n=0..44.

Formula

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

Example

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;

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

Crossrefs

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

Sequence in context: A159788 A179112 A359119 * A096612 A218707 A177153

Adjacent sequences: A387123 A387124 A387125 * A387127 A387128 A387129

Keyword

nonn,tabl

Author

Peter Luschny, Aug 18 2025

Status

approved