= Gaussian even-moment pairing count
{c}
{title2=$\mathbb EX^{2n}=(2n-1)!!\,v^n$}
For a centered scalar <normal random variable> of <variance> $v$, the <Isserlis theorem> sums complete pairings of $2n$ factors. The first factor has $2n-1$ partners, then $2n-3$ choices remain for the first unpaired factor, giving $(2n-1)!!=(2n)!/(2^nn!)$. Odd moments vanish. Summing the <moment-generating function> gives $\exp(vs^2/2)$. This is a scalar formula, not a formula for the length of a vector.
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