A268920 Denominators of the rational number triangle R(n, k) = (n^4 - 30*n^2*k^2 + 60*n*k^3 - 30*k^4) / (120*n), n >= 1, k = 1, ..., n.

120, 120, 15, 120, 120, 40, 240, 15, 240, 15, 120, 120, 120, 120, 24, 120, 15, 40, 15, 120, 5, 840, 840, 840, 840, 840, 840, 120, 480, 30, 480, 15, 480, 30, 480, 15, 360, 360, 40, 360, 360, 40, 360, 360, 40, 120, 15, 120, 15, 24, 15, 120, 15, 120, 3, 1320, 1320, 1320, 1320, 1320, 1320, 1320, 1320, 1320, 1320, 120, 240, 15, 80, 15, 240, 5, 240, 15, 80, 15, 240, 5

Offset

1,1

Comments

For the numerator triangle see A268919.

For details and the Hurwitz reference see A267863.

Links

G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Formula

T(n, k) = denominator(R(n, k)) with the rational triangle R(n, k) = (n^4 - 30*n^2*k^2 + 60*n*k^3 - 30*k^4)/(120*n), n >= 1, k = 1, ..., n.

Example

The triangle T(n, k) begins:
  n\k   1   2   3   4   5   6   7   8   9  10 ...
  1:  120
  2:  120  15
  3:  120 120  40
  4:  240  15 240  15
  5:  120 120 120 120  24
  6:  120  15  40  15 120   5
  7:  840 840 840 840 840 840 120
  8:  480  30 480  15 480  30 480  15
  9:  360 360  40 360 360  40 360 360 40
  10: 120  15 120  15  24  15 120  15 120   3
  ...
For the triangle of the rationals R(n, k) see A268919.

Mathematica

Flatten[Table[(m^4-30m^2 k^2+60m k^3-30k^4)/(120m), {m, 15}, {k, m}]]// Denominator (* Harvey P. Dale, Mar 03 2020 *)

Prog

(Magma)
A268920:= func< n, k | Denominator((n^4-30*n^2*k^2+60*n*k^3-30*k^4)/(120*n)) >;
[A268920(n, k): k in [1..n], n in [1..15]]; // G. C. Greubel, Oct 05 2024
(SageMath)
def A268920(n, k): return denominator((n^4-30*n^2*k^2+60*n*k^3-30*k^4)/(120*n))
flatten([[A268920(n, k) for k in range(1, n+1)] for n in range(1, 16)]) # G. C. Greubel, Oct 05 2024

Crossrefs

Cf. A267863, A268919 (numerators).

Sequence in context: A332417 A244950 A174149 * A332560 A334571 A056466

Adjacent sequences: A268917 A268918 A268919 * A268921 A268922 A268923

Keyword

nonn,frac,tabl,easy

Author

Wolfdieter Lang, Feb 25 2016

Status

approved