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 A378834 #8 Dec 12 2024 09:30:53
%S A378834 1,3,2,2,2,6,6,32,32,240,240,2304,2304
%N A378834 Number of ways to reverse a permutation of n elements by the minimum number of steps of rotate left or right 1 place (L,R), or exchange first two elements (E).
%C A378834 The minimum number of steps is A186752(n).
%C A378834 For n=2, steps L,R,E all have the same effect but each is taken as a separate way so that a(2) = 3.
%C A378834 For 4 <= n <= 13, a(n) = (h+2)*2^h*h! where h = floor((n-4)/2).
%e A378834 For n=1, permutation {1} is already its own reversal so has a(1) = 1 way of no steps (A186752(1) = 0).
%e A378834 For n=5, the a(5) = 2 ways to reverse {1,2,3,4,5} by A186752(5) = 8 steps are
%e A378834 E, L, L, E, L, E, R, E
%e A378834 E, L, E, R, E, R, R, E
%e A378834 Notice these are inverses: reverse the order and flip L<->R in one makes the other.
%Y A378834 Cf. A186752 (number of steps).
%Y A378834 Cf. A061545 (ways for LE).
%K A378834 nonn,more
%O A378834 1,2
%A A378834 _Kevin Ryde_, Dec 09 2024