Egan, meanwhile, got a simple formula for the \\(n\\)th moment in the \\(d = 2\\) case, at least when \\(n\\) is even:

> As well as: moment(4,n) = Catalan(n/2+1) we have: moment(2,n) = \\(n \choose {n/2}\\).

That gives these numbers:

$$ 2, 6, 10, 70 , 252, \dots $$

Straight down the middle of Pascal's triangle!

> As well as: moment(4,n) = Catalan(n/2+1) we have: moment(2,n) = \\(n \choose {n/2}\\).

That gives these numbers:

$$ 2, 6, 10, 70 , 252, \dots $$

Straight down the middle of Pascal's triangle!