[seqfan] Interesting sequence

[David Wilson]

Starting with integer n,  multiply by ((n+1)/n), take the floor, multiply by
(n/(n-1), take the floor, all the way down to 2/1, call the result f(n).

For example, starting with n = 5

floor(5*(6/5)) = 6,
floor(6*(5/4)) = 7,
floor(7*(4/3)) = 9,
floor(9*(3/2)) = 13,
floor(14*(2/1)) = 26.

so f(5) = 26.

Starting at n = 1, we have

f = (2, 6,  12, 18, 26, 38, 48, 62, 78, 90, ...)

It's trivial that all elements are even, given the final multiplier 2/1.

It looks to me as if f(n) ~ pi*n^2/4, but I couldn't begin to prove this.