A062097 a(1) = 1; a(n) = sum of the sum and the product of all previous terms.

1, 2, 5, 18, 206, 37312, 1383566504, 1914204327753559888, 3664178205741957271429583378492509856, 13426201923434349344563612023870972836592501276745812341399323779519061312

Offset

1,2

Comments

The next term has 147 digits. [From Harvey P. Dale, Nov 01 2011]

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..13

Formula

For n>=4, a(n) = 2*a(n-1) + a(n-2)*(a(n-1) - 2*a(n-2))*(a(n-1) -1)/(a(n-2) -1). - Leroy Quet, Nov 27 2007

Example

a(4)=18 as 18 = {1+2+5} + {1*2*5}, where 1, 2, 5 are the previous terms.

Mathematica

lf[l_List] := Append[l, Plus @@ l + Times @@ l]; Nest[f, {1}, 9] (* Harvey P. Dale, Nov 01 2011 *) and modified by Robert G. Wilson v, Sep 03 2012

Prog

(PARI) A062097(n, s=0, p=1)={for(n=2, n, p*=-s+s+=s+p); p+s} \\ - M. F. Hasler, Sep 03 2012
(Haskell)
a062097 n = a062097_list !! (n-1)
a062097_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. A057194.

Sequence in context: A097584 A197855 A289126 * A356366 A323706 A125765

Adjacent sequences: A062094 A062095 A062096 * A062098 A062099 A062100

Keyword

nonn,easy

Author

Amarnath Murthy, Jun 19 2001

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 19 2001

More terms from Harvey P. Dale, Nov 01 2011

Status

approved