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A057194 a(1) = 1; a(n+1) = (Product_{k=1..n} a(k)) * Sum_{k=1..n} a(k). 4
1, 1, 2, 8, 192, 626688, 1206883411034112, 2804162815248299020572908137501717168128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Conjecture: a(n) < A216151(n) for all n > 1. - Jon Perry, Sep 12 2012

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..11

FORMULA

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

EXAMPLE

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.

MATHEMATICA

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 *)

PROG

(PARI)

v=vector(12, n, 1);

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

v057194=v

/* Joerg Arndt, Sep 03 2012 */

(Haskell)

a057194 n = a057194_list !! (n-1)

a057194_list = 1 : f 1 1 where

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

-- Reinhard Zumkeller, Mar 20 2014

CROSSREFS

Cf. A062097, A216151.

Cf. A058345.

Sequence in context: A234637 A234632 A070235 * A012539 A012535 A012300

Adjacent sequences:  A057191 A057192 A057193 * A057195 A057196 A057197

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 15 2000

STATUS

approved

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Last modified May 9 13:09 EDT 2021. Contains 343742 sequences. (Running on oeis4.)