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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

%I #18 Oct 06 2024 09:15:37

%S 120,120,15,120,120,40,240,15,240,15,120,120,120,120,24,120,15,40,15,

%T 120,5,840,840,840,840,840,840,120,480,30,480,15,480,30,480,15,360,

%U 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

%N 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.

%C For the numerator triangle see A268919.

%C For details and the Hurwitz reference see A267863.

%H G. C. Greubel, <a href="/A268920/b268920.txt">Rows n = 1..50 of the triangle, flattened</a>

%F 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.

%e The triangle T(n, k) begins:

%e n\k 1 2 3 4 5 6 7 8 9 10 ...

%e 1: 120

%e 2: 120 15

%e 3: 120 120 40

%e 4: 240 15 240 15

%e 5: 120 120 120 120 24

%e 6: 120 15 40 15 120 5

%e 7: 840 840 840 840 840 840 120

%e 8: 480 30 480 15 480 30 480 15

%e 9: 360 360 40 360 360 40 360 360 40

%e 10: 120 15 120 15 24 15 120 15 120 3

%e ...

%e For the triangle of the rationals R(n, k) see A268919.

%t 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 *)

%o (Magma)

%o A268920:= func< n,k | Denominator((n^4-30*n^2*k^2+60*n*k^3-30*k^4)/(120*n)) >;

%o [A268920(n,k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Oct 05 2024

%o (SageMath)

%o def A268920(n,k): return denominator((n^4-30*n^2*k^2+60*n*k^3-30*k^4)/(120*n))

%o flatten([[A268920(n,k) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Oct 05 2024

%Y Cf. A267863, A268919 (numerators).

%K nonn,frac,tabl,easy

%O 1,1

%A _Wolfdieter Lang_, Feb 25 2016