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A305851 a(n) = (a(n-1)+a(n-2))^(n-2) with a(1)=a(2)=1.

%I A305851 #31 Nov 03 2022 13:51:34
%S A305851 1,1,2,9,1331,3224179360000,
%T A305851 348414297354956334043085401797347258376901025074126347562215651
%N A305851 a(n) = (a(n-1)+a(n-2))^(n-2) with a(1)=a(2)=1.
%C A305851 a(8) has 376 digits, a(9) has 2627 digits, a(10) has 21015 digits, see b-file and a-file. - _Eric Chen_, Jun 14 2018
%H A305851 Eric Chen, <a href="/A305851/b305851.txt">Table of n, a(n) for n = 1..9</a>
%H A305851 Eric Chen, <a href="/A305851/a305851.txt">Table of n, a(n) for n = 1..10</a> (an a-file)
%F A305851 a(n) ~ c^((n-2)!), where c = 3.3203520468282576446980958620234685911457954899308569085994... - _Vaclav Kotesovec_, Jul 23 2018
%t A305851 Nest[Append[#, (#[[-1]] + #[[-2]] )^(Length@ # - 2)] &, {1, 1}, 6] (* _Michael De Vlieger_, Jun 11 2018 *)
%t A305851 RecurrenceTable[{a[n] == (a[n-1] + a[n-2])^(n-2), a[1] == 1, a[2] == 1}, a, {n, 1, 7}] (* _Vaclav Kotesovec_, Jul 23 2018 *)
%t A305851 nxt[{n_,a_,b_}]:={n+1,b,(a+b)^(n-1)}; NestList[nxt,{1,1,1},7][[All,2]] (* _Harvey P. Dale_, Nov 03 2022 *)
%o A305851 (Python)
%o A305851 #Generates and prints a list containing the terms, up to the term with the index of seq_limit
%o A305851 seq_limit=9
%o A305851 seq_list=[1,1]
%o A305851 for seq_no in range(3,seq_limit):
%o A305851     seq_list.append((seq_list[-1]+seq_list[-2])**(seq_no-2))
%o A305851 print(seq_list)
%o A305851 (PARI) a(n)=if(n<3,1,(a(n-1)+a(n-2))^(n-2)) \\ _Eric Chen_, Jun 14 2018
%Y A305851 Cf. A050923.
%K A305851 nonn,easy,less
%O A305851 1,3
%A A305851 _Yigithan TAMER_, Jun 11 2018