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 A057194 a(1) = 1; a(n+1) = (Product_{k=1..n} a(k)) * Sum_{k=1..n} a(k). 4

%I

%S 1,1,2,8,192,626688,1206883411034112,

%T 2804162815248299020572908137501717168128

%N a(1) = 1; a(n+1) = (Product_{k=1..n} a(k)) * Sum_{k=1..n} a(k).

%C Conjecture: a(n) < A216151(n) for all n > 1. - _Jon Perry_, Sep 12 2012

%C a(n) is about x^y^n with y = phi^2 = 2.61803398874... and x around 1.04200817421788490539. - _Charles R Greathouse IV_, Sep 12 2012

%H Reinhard Zumkeller, <a href="/A057194/b057194.txt">Table of n, a(n) for n = 1..11</a>

%F For n > 1; a(n+2) = a(n+1)^2 * ( a(n+1)/a(n) - a(n) + 1 ).

%e a(5) = (a(1)*a(2)*a(3)*a(4)) * (a(1)+a(2)+a(3)+a(4)) = 1*1*2*8 * (1+1+2+8) = 192.

%t a[1] = 1; a[n_] := Product[a[i], {i, n - 1}] Sum[a[i], {i, n - 1}]; Array[a, 10] (* _Robert G. Wilson v_, Sep 03 2012 *)

%o (PARI)

%o v=vector(12,n,1);

%o for (n=3,#v, v[n] = prod(k=1,n-1, v[k]) * sum(k=1,n-1, v[k] ) );

%o v057194=v

%o /* _Joerg Arndt_, Sep 03 2012 */

%o a057194 n = a057194_list !! (n-1)

%o a057194_list = 1 : f 1 1 where

%o f u v = w : f (u * w) (v + w) where w = u * v

%o -- _Reinhard Zumkeller_, Mar 20 2014

%Y Cf. A062097, A216151.

%Y Cf. A058345.

%K nonn

%O 1,3

%A _Leroy Quet_, Sep 15 2000

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Last modified June 12 06:52 EDT 2021. Contains 344943 sequences. (Running on oeis4.)