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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.
5
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.
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
KEYWORD
nonn,frac,tabl,easy
AUTHOR
Wolfdieter Lang, Feb 25 2016
STATUS
approved