A062097 - OEIS

%I #18 Apr 09 2014 10:16:38

%S 1,2,5,18,206,37312,1383566504,1914204327753559888,

%T 3664178205741957271429583378492509856,

%U 13426201923434349344563612023870972836592501276745812341399323779519061312

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

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

%H Reinhard Zumkeller, <a href="/A062097/b062097.txt">Table of n, a(n) for n = 1..13</a>

%F 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

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

%t 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

%o (PARI) A062097(n,s=0,p=1)={for(n=2,n,p*=-s+s+=s+p);p+s} \\ - _M. F. Hasler_, Sep 03 2012

%o (Haskell)

%o a062097 n = a062097_list !! (n-1)

%o a062097_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. A057194.

%K nonn,easy

%O 1,2

%A _Amarnath Murthy_, Jun 19 2001

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

%E More terms from Harvey P. Dale, Nov 01 2011