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%I #29 Jan 03 2021 14:08:19
%S 1,2,6,108,151632,29820965660928,174758887882787264327879044178706432
%N a(n+1) = (Product_{k=1..n} a(k)) * Sum_{k=1..n} a(k), a(1)=1, a(2)=2.
%C Conjecture: a(n) > A057194(n) for all n > 1.
%C 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
%H Alois P. Heinz, <a href="/A216151/b216151.txt">Table of n, a(n) for n = 1..10</a>
%e a(4) = 108 = (6+2+1)*(6*2*1).
%p a:= proc(n) a(n):= `if`(n<3, n,
%p mul(a(k), k=1..n-1) * add(a(k), k=1..n-1))
%p end:
%p seq (a(n), n=1..10); # _Alois P. Heinz_, Sep 12 2012
%t t = {1, 2}; Do[AppendTo[t, (Plus @@ t) (Times @@ t)], {5}]; t (* _T. D. Noe_, Sep 04 2012 *)
%o (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
%o (Haskell)
%o a216151 n = a216151_list !! (n-1)
%o a216151_list = 1 : 2 : f 2 3 where
%o f u v = w : f (u * w) (v + w) where w = u * v
%o -- _Reinhard Zumkeller_, Mar 20 2014
%Y Cf. A057194.
%K nonn
%O 1,2
%A _Jon Perry_, Sep 02 2012
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