A216151 a(n+1) = (Product_{k=1..n} a(k)) * Sum_{k=1..n} a(k), a(1)=1, a(2)=2.

1, 2, 6, 108, 151632, 29820965660928, 174758887882787264327879044178706432

Offset

1,2

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10

Example

a(4) = 108 = (6+2+1)*(6*2*1).

Maple

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

Mathematica

t = {1, 2}; Do[AppendTo[t, (Plus @@ t) (Times @@ t)], {5}]; t (* T. D. Noe, Sep 04 2012 *)

Prog

(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

Crossrefs

Cf. A057194.

Sequence in context: A222854 A351780 A059088 * A057771 A056164 A156500

Adjacent sequences: A216148 A216149 A216150 * A216152 A216153 A216154

Keyword

nonn

Author

Jon Perry, Sep 02 2012

Status

approved