Curious short pattern in least common multiple of binomial coefficients

Question

$$f(n) = \text{lcm}\Bigg(\binom n 1, \binom n 2, \dots,\binom n n\Bigg)$$

If we list $f(n) =\; $$\text{A002944}$$(n)$ it starts of kind of boring, but at $n = 14$ we see a curious pattern in base $10$, only for four numbers (I added leading zeros for clarity):

\begin{array}{rcr} f(14) &=& 024024\\ f(15) &=& 045045\\ f(16) &=& 720720\\ f(17) &=& 680680 \end{array}

Is this just dumb luck and I'm seeing a pattern in noise? Or is there an explanation why this 'echo' pattern occurs?

Answer 1

This pattern of $xy0xy$ (which occurs often in pascals triangle) comes from the fact that $1001$ is the product of a sequence of small primes that don't cancel out for small values.

$1001=7 \times 11 \times 13$