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A049384
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a(0)=1, a(n+1)=(n+1)^a(n)
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12
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OFFSET
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0,3
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COMMENTS
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An "exponential factorial".
Might also be called the "expofactorial" of n. - Walter Arrighetti (walter.arrighetti(AT)fastwebnet.it), Jan 16 2006
The next term is too large to include.
The next term (a(5)) has 183,231 digits. - Harvey P. Dale, May 26 2013
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REFERENCES
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David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons, Problem 11286, Amer. Math. Monthly, 116 (2009) 466-467.
David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 393-402.
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LINKS
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Table of n, a(n) for n=0..4.
David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing (arXiv:math.NT/0611293).
Walter Arrighetti, LabCEM, Department of Electronic Engineering, Univ. degli Studi di Roma "La Sapienza".
Walter Arrighetti, Double Vision [Broken link?]
Vladimir Orlovsky, Very Big Number, Feb 19 1999
Eric Weisstein's World of Mathematics, Exponential Factorial
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EXAMPLE
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a(4) = 4^9 = 262144.
a(5) = 5^262144 has 183231 decimal digits. - Rick L. Shepherd, Feb 15 2002
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MATHEMATICA
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Expofactorial[0] := 1; Expofactorial[n_Integer] := n^Expofactorial[n - 1]; Table[Expofactorial[n], {n, 0, 4}] (* Walter Arrighetti, Jan 24 2006 *)
nxt[{n_, a_}]:={n+1, (n+2)^a}; Transpose[NestList[nxt, {0, 1}, 4]][[2]] (* Harvey P. Dale, May 26 2013 *)
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CROSSREFS
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Cf. A000142.
Sequence in context: A028581 A030252 * A132859 A103562 A140319 A120314
Adjacent sequences: A049381 A049382 A049383 * A049385 A049386 A049387
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KEYWORD
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nonn
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AUTHOR
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Marcel Jackson (Marcel.Jackson(AT)utas.edu.au)
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STATUS
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approved
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