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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.

A338522 Number of cyclic Latin squares of order n.

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%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