how can I rewrite, and optimize, this EMA calculation in F#

this is an EMA calculation:

let EMA (period : int) (data : double[]) : double[] =
    let multiplier = 2.0 / (double)(period + 1)
    let output = Array.create data.Length System.Double.NaN 

    output.[period - 1] <- data.[0..period - 1] |> Seq.average
    for i in seq {period .. (data.Length - 1)} do
        output.[i] <- (data.[i] * multiplier) + (output.[i - 1] * (1. - multiplier))

    output

you can test it with:

EMA 3 [|1.;3.;4.;7.;5.;6.;9.;8.|]

and it gives:

[|NaN;Nan;2.66.;4.83;4.91;5.45;7.22;7.61|]

my first question is regarding the loop at the end:

for i in seq {period .. (data.Length - 1)} do
    output.[i] <- (data.[i] * multiplier) + (output.[i - 1] * (1. - multiplier))

can this be rewritten using a sequence operator?

my second question is: is there a fast F# implementation floating around? I couldn't find any.