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 A338522 #22 Mar 25 2022 14:38:31 %S A338522 1,2,12,48,480,1440,30240,161280,2177280,14515200,399168000, %T A338522 1916006400,74724249600,523069747200,10461394944000,167382319104000, %U A338522 5690998849536000,38414242234368000,2189611807358976000,19463216065413120000,613091306060513280000 %N A338522 Number of cyclic Latin squares of order n. %C A338522 A cyclic Latin square is a Latin square in which row i is obtained by cyclically shifting row i-1 by d places. %C A338522 Equivalently, a Latin square is cyclic if and only if each row is a cyclic permutation of the first row and each column is a cyclic permutation of the first column. %H A338522 Eduard I. Vatutin, <a href="http://evatutin.narod.ru/evatutin_ls_euler_func.pdf">Enumerating cyclic Latin squares and Euler totient function calculating using them</a>, High-performance computing systems and technologies, 2020, Vol. 4, No. 2, pp. 40-48. (in Russian) %H A338522 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_1427">About the number of cyclic Latin squares and cyclic diagonal Latin squares</a> (in Russian). %F A338522 a(n) = phi(n) * n!. %F A338522 a(n) = A000010(n) * A000142(n). %e A338522 For n=5 there are 4 cyclic Latin squares with the first row in natural order: %e A338522 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 %e A338522 1 2 3 4 0 2 3 4 0 1 3 4 0 1 2 4 0 1 2 3 %e A338522 2 3 4 0 1 4 0 1 2 3 1 2 3 4 0 3 4 0 1 2 %e A338522 3 4 0 1 2 1 2 3 4 0 4 0 1 2 3 2 3 4 0 1 %e A338522 4 0 1 2 3 3 4 0 1 2 2 3 4 0 1 1 2 3 4 0 %e A338522 and 4*5! = 480 cyclic Latin squares. %Y A338522 Cf. A000010, A000142, A074930, A123565. %K A338522 nonn,easy %O A338522 1,2 %A A338522 _Eduard I. Vatutin_, Nov 01 2020