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 A074456 #11 Jun 08 2023 08:52:01 %S A074456 3,3,1,6,1,1,9,4,4,8,4,9,6,2,0,0,2,6,9,1,8,6,3,0,2,4,0,1,5,5,8,2,9,7, %T A074456 3,5,8,0,0,4,7,2,3,2,8,4,1,0,8,7,2,5,8,5,1,3,1,0,0,1,1,8,1,5,5,4,0,3, %U A074456 7,5,6,5,4,6,4,7,1,8,4,3,4,4,6,6,6,0,7,4,6,0,9,4,9,3,5,1,3,8,7 %N A074456 Consider surface area of unit sphere as a function of the dimension d; maximize this as a function of d (considered as a continuous variable); sequence gives decimal expansion of the resulting surface area. %C A074456 If you set v[n_] := Pi^(n/2)/(n/2)! and s[n_] := n*Pi^(n/2)/(n/2)! and then Plot[{6.283v[n - 2], s[n]}, {n, 0, 20}], the two curves are almost identical. %e A074456 33.1611944849620026918630240155829735800472328410872... %t A074456 area[d_] := d * Pi^(d/2)/Gamma[d/2 + 1]; area[x /. FindRoot[PolyGamma[x/2] == Log[Pi], {x, 7}, WorkingPrecision -> 120]] (* _Amiram Eldar_, Jun 08 2023 *) %Y A074456 The dimension is given in A074455. %Y A074456 Cf. A072478, A072479, A074454. %K A074456 cons,nonn %O A074456 2,1 %A A074456 _Robert G. Wilson v_, Aug 22 2002 %E A074456 Checked by _Martin Fuller_, Jul 12 2007