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a(n) = floor(b(n)) where b(-1)=2, b(n)=b(n-1)^2-n^b(n-1).
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%I #14 Sep 06 2023 09:43:41

%S 2,4,15,-32543,1059046848

%N a(n) = floor(b(n)) where b(-1)=2, b(n)=b(n-1)^2-n^b(n-1).

%C a(4) ~ -5.3069609889*10^637609736, and is too large for display. - _D. S. McNeil_, Nov 28 2010

%t a=2;lst={};Do[a=a^2-n^a;AppendTo[lst,Floor[a]],{n,0,3}];lst

%o (PARI) print1(a=2); for(n=0,3,print1(", "floor(a=a^2-n^a)))

%Y Cf. A153059, A086851, A153060, A098152, A028300, A153061, A153062, A153063

%K sign

%O -1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008

%E Definition clarified by _R. J. Mathar_ and _M. F. Hasler_, Nov 27 2010