A268918 Denominators of the rational number triangle R(n, k) = - k*(n - k)*(n - 2*k)/(6*n), n >= 1, k = 1, ..., n.

1, 1, 1, 9, 9, 1, 4, 1, 4, 1, 5, 5, 5, 5, 1, 9, 9, 1, 9, 9, 1, 7, 7, 7, 7, 7, 7, 1, 8, 1, 8, 1, 8, 1, 8, 1, 27, 27, 1, 27, 27, 1, 27, 27, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 36, 9, 4, 9, 36, 1, 36, 9, 4, 9, 36, 1, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1

Offset

1,4

Comments

For the numerators see A268917.

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 R(n, k) = - k*(n - k)*(n - 2*k)/(6*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  11  12 ...
  1:    1
  2:    1  1
  3:    9  9  1
  4:    4  1  4  1
  5:    5  5  5  5  1
  6:    9  9  1  9  9  1
  7:    7  7  7  7  7  7  1
  8:    8  1  8  1  8  1  8  1
  9:   27 27  1 27 27  1 27 27  1
  10:   5  5  5  5  1  5  5  5  5  1
  11:  11 11 11 11 11 11 11 11 11 11   1
  12:  36  9  4  9 36  1 36  9  4  9  36   1
  ...
For the triangle of the rationals R(n, k) see A268917.

Mathematica

Denominator@ Table[-k (m - k) (m - 2 k)/(6 m), {m, 17}, {k, m}] // Flatten (* Michael De Vlieger, Feb 26 2016 *)

Prog

(PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(denominator(- k*(n-k)*(n-2*k)/(6*n)), ", "); ); print(); ); } \\ Michel Marcus, Feb 26 2016
(Magma)
A268918:= func< n, k | Denominator(k*(k-n)*(n-2*k)/(6*n)) >;
[A268918(n, k): k in [1..n], n in [1..17]]; // G. C. Greubel, Oct 04 2024
(SageMath)
def A268918(n, k): return denominator(k*(k-n)*(n-2*k)/(6*n))
flatten([[A268918(n, k) for k in range(1, n+1)] for n in range(1, 18)]) # G. C. Greubel, Oct 04 2024

Crossrefs

Cf. A268917.

Sequence in context: A280554 A195722 A133627 * A144982 A228788 A019788

Adjacent sequences: A268915 A268916 A268917 * A268919 A268920 A268921

Keyword

nonn,frac,tabl,easy

Author

Wolfdieter Lang, Feb 25 2016

Extensions

More terms added by G. C. Greubel, Oct 04 2024

Status

approved