This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A264930 #17 Jan 11 2020 15:57:47 %S A264930 1,2,4,27,340282366920938463463374607431768211456 %N A264930 a(n) = n<n>n where x<n>y is a right associative hyperoperation. %C A264930 Define x<n>y recursively as follows (this is a right associative version): %C A264930 x<0>y = x+1; %C A264930 x<1>0 = x; %C A264930 x<2>0 = 0; %C A264930 x<n>y = ( x<n>(y-1) ) <n-1> x for n>0 and y>0. %C A264930 We have: %C A264930 x<1>y = (...((x<0>y)<0>y)...y)(y nested parenthesis) = x+y; %C A264930 x<2>y = (...((x<1>y)<1>y)...y)(y nested parenthesis) = x*y; %C A264930 x<3>y = (...((x<2>y)<2>y)...y)(y nested parenthesis) = x^y; %C A264930 x<4>y = (...((x<3>y)<3>y)...y)(y nested parenthesis) = (...((x^x)^x)...^x) (a height-y bottom-up tower power, NOT tetration) = x^x^(y-1). %C A264930 ... %H A264930 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hyperoperation">Hyperoperations</a>. %e A264930 a(0) = 0+1 = 1; %e A264930 a(1) = 1+1 = 2; %e A264930 a(2) = 2*2 = 4; %e A264930 a(3) = 3^3 = 27; %e A264930 a(4) = ((4^4)^4)^4 = 340282366920938463463374607431768211456; %e A264930 a(5) = 5<5>5 = (((((5<4>5)<4>5)<4>5)<4>5)<4>5)<4>5. %Y A264930 Cf. A054871, A189896. %K A264930 nonn %O A264930 0,2 %A A264930 _Natan Arie Consigli_, Nov 29 2015