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

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

Table of n, a(n) for n=1..78.

Formula

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

Example

The triangle T(m, a) begins:
m\a   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(m, a) see A268919.

Mathematica

Flatten[Table[(m^4-30m^2 a^2+60m a^3-30a^4)/(120m), {m, 12}, {a, m}]]// Denominator (* Harvey P. Dale, Mar 03 2020 *)

Crossrefs

Cf. 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