A387138 - OEIS

A387138

Triangle read by rows: T(n, k) = binomial(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, 2, 6, 18, 18, 6, 12, 48, 72, 48, 12, 60, 300, 600, 600, 300, 60, 360, 2160, 5400, 7200, 5400, 2160, 360, 2520, 17640, 52920, 88200, 88200, 52920, 17640, 2520, 5040, 40320, 141120, 282240, 352800, 282240, 141120, 40320, 5040

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OFFSET

0,4

LINKS

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

FORMULA

T(n, k) = A048803(n) * A007318(n, k).

EXAMPLE

Triangle begins:

[0] 1;

[1] 1, 1;

[2] 2, 4, 2;

[3] 6, 18, 18, 6;

[4] 12, 48, 72, 48, 12;

[5] 60, 300, 600, 600, 300, 60;

[6] 360, 2160, 5400, 7200, 5400, 2160, 360;

[7] 2520, 17640, 52920, 88200, 88200, 52920, 17640, 2520;

[8] 5040, 40320, 141120, 282240, 352800, 282240, 141120, 40320, 5040;

MAPLE

A387138 := (n, k) -> binomial(n, k) * mul(NumberTheory:-Radical(j), j = 1..n):

MATHEMATICA

A387138[n_, k_] := Binomial[n, k] Times @@ ResourceFunction["IntegerRadical"][Range[1, n]];

Table[A387138[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

CROSSREFS

Cf. A007318 (binomial), A007947 (radical), A048803 (column 0 and main diagonal), A387139 (row sums), A387126.

Sequence in context: A138024 A167656 A253666 * A174298 A196347 A021012

Adjacent sequences: A387135 A387136 A387137 * A387139 A387140 A387141

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Aug 18 2025

STATUS

approved