A320637 Regular triangle read by rows: T(n,k) = Lcm_{m=k..n} d(n,k) where d(n,k) is the denominator of the unsigned Stirling1(n,k)*k!/n! for 0 <= k <= n.

1, 1, 1, 1, 2, 1, 1, 6, 1, 1, 1, 12, 12, 2, 1, 1, 60, 12, 4, 1, 1, 1, 60, 180, 8, 6, 2, 1, 1, 420, 180, 120, 6, 6, 1, 1, 1, 840, 5040, 240, 240, 6, 4, 2, 1, 1, 2520, 5040, 15120, 240, 144, 4, 12, 1, 1, 1, 2520, 25200, 30240, 15120, 288, 240, 24, 3, 2, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Abdelmalek Bedhouche and Bakir Farhi, On some products taken over the prime numbers, arXiv:2207.07957 [math.NT], 2022.

Bakir Farhi, On the derivatives of the integer-valued polynomials, arXiv:1810.07560 [math.NT], 2018. See Table 1 c(n,k) p. 15.

Example

Triangle begins:
  1,
  1, 1,
  1, 2, 1,
  1, 6, 1, 1,
  1, 12, 12, 2, 1,
  1, 60, 12, 4, 1, 1,
  1, 60, 180, 8, 6, 2, 1,
  1, 420, 180, 120, 6, 6, 1, 1,
  ...

Prog

(PARI) d(n, k) = denominator(abs(stirling(n, k, 1))*k!/n!);
T(n, k) = my(x = 1); for (m=k, n, x = lcm(x, d(m, k))); x;

Crossrefs

Cf. A000254, A003418, A141412.

Sequence in context: A338036 A216914 A216917 * A216919 A152656 A096162

Adjacent sequences: A320634 A320635 A320636 * A320638 A320639 A320640

Keyword

nonn,tabl

Author

Michel Marcus, Oct 18 2018

Extensions

Corrected by Michel Marcus, Jul 19 2022

Status

approved