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A216151
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a(n+1) = (Product_{k=1..n} a(k)) * Sum_{k=1..n} a(k), a(1)=1, a(2)=2.
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2
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OFFSET
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1,2
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COMMENTS
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Conjecture: a(n) > A057194(n) for all n > 1.
a(n) is about x^y^n with y = phi^2 = 2.61803398874... and x around 1.101029823705009804368. - Charles R Greathouse IV, Sep 12 2012
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..10
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EXAMPLE
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a(4) = 108 = (6+2+1)*(6*2*1).
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MAPLE
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a:= proc(n) a(n):= `if`(n<3, n,
mul(a(k), k=1..n-1) * add(a(k), k=1..n-1))
end:
seq (a(n), n=1..10); # Alois P. Heinz, Sep 12 2012
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MATHEMATICA
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t = {1, 2}; Do[AppendTo[t, (Plus @@ t) (Times @@ t)], {5}]; t (* T. D. Noe, Sep 04 2012 *)
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PROG
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(PARI) v=vector(10, i, i); for(i=3, #v, v[i] = prod(j=1, i-1, v[j])*sum(j=1, i-1, v[j])); v \\ Charles R Greathouse IV, Sep 12 2012
(Haskell)
a216151 n = a216151_list !! (n-1)
a216151_list = 1 : 2 : f 2 3 where
f u v = w : f (u * w) (v + w) where w = u * v
-- Reinhard Zumkeller, Mar 20 2014
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CROSSREFS
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Cf. A057194.
Sequence in context: A181036 A222854 A059088 * A057771 A056164 A156500
Adjacent sequences: A216148 A216149 A216150 * A216152 A216153 A216154
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KEYWORD
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nonn
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AUTHOR
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Jon Perry, Sep 02 2012
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STATUS
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approved
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