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a(1) = a(2) = 1; a(n) = a(n-1) + a(n-2)! for n > 2.
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%I #4 Apr 22 2014 14:13:50

%S 1,1,2,3,5,11,131,39916931

%N a(1) = a(2) = 1; a(n) = a(n-1) + a(n-2)! for n > 2.

%C The next term (a(9)) has 222 digits. - _Harvey P. Dale_, Apr 22 2014

%t a = {1, 1}; For[i = 3, i <= 8, i++, c = (a[[i - 1]] + a[[i - 2]]!); a = Append[a, c]]; a

%t RecurrenceTable[{a[1]==a[2]==1,a[n]==a[n-1]+a[n-2]!},a,{n,8}] (* _Harvey P. Dale_, Apr 22 2014 *)

%K nonn

%O 1,3

%A _Joseph L. Pe_, Oct 17 2002