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A005831
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a(n+1) = a(n) * (a(n-1) + 1).
(Formerly M1264)
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3
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0, 1, 1, 2, 4, 12, 60, 780, 47580, 37159980, 1768109008380, 65702897157329640780, 116169884340604934905464739377180, 7632697963609645128663145969343357330533515068777580, 886689639639303288926299195509965193299034793881606681727875910370940270908216401980
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OFFSET
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0,4
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COMMENTS
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A discrete analog of the derivative of t(x) = tetration base e, since t'(x) = t(x) * t(x-1) * t(x-2) * ... y = y * exp(y) * exp(exp(y)) * ... * t(x) This sequence satisfies almost the same equation but the derivative is replaced by a difference, comparable to the relations between differential equations and their associated difference equations. - Raes Tom (tommy1729(AT)hotmail.com), Aug 06 2008
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(0) = a(1) = 1, a(2) = 2; a(n) = a(n-1)*a(n-2)*a(n-3)*... + a(n-1). - Raes Tom (tommy1729(AT)hotmail.com), Aug 06 2008
The sequence grows like a doubly exponential function, similar to Sylvester's sequence. In fact we have the asymptotic form : a(n) ~ e ^ (Phi ^ n) where e and Phi are the best possible constants. - Raes Tom (tommy1729(AT)hotmail.com), Aug 06 2008
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EXAMPLE
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a(5) = 12 since 12 = 1*2*4 + 4.
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MATHEMATICA
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RecurrenceTable[{a[0]==0, a[1]==1, a[n]==a[n-1](a[n-2]+1)}, a, {n, 15}] (* Harvey P. Dale, Aug 17 2013 *)
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PROG
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(Haskell)
a005831 n = a005831_list !! n
a005831_list = 0:1:zipWith (*) (tail a005831_list) (map succ a005831_list)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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