Talk:Exponential factorial

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I would like to believe that Jddowney789 removed a 1 digit from the sum of reciprocals because he or she honestly believed that the calculation was incorrect. In that case, the calculation methodology has to be explained. I don't know how Anton Mravcek did the calculation, but here is what I did to doublecheck it. Using Mathematica, I defined the following:

a[0] := 1 a[n_] := a[n] = n^(a[n - 1])

These should look a lot like the formula given in the article. Then

Table[a[n], {n, 4}]

lets me know that the definitions are correct. Then,

1/%

(the percent symbol in Mathematica refers to the previous calculation) gives me a list of fractions, then

N[Plus@@%,23]

gives 1.6111149258083767361111. Then I put in

"

then paste the number from Wikipedia, followed by

" == "

and copy and paste the number from the calculation above. I hit enter, and Mathematica says True.

But to be extra sure, I also compare the number against that given in the OEIS sequence A080219 (to strip the commas, click on the blue "cons" link). PrimeFan 21:54, 17 February 2006 (UTC)