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%I #10 Oct 01 2017 13:19:15
%S 1,1,2,6,36,325,3924,58996,1049088,21526641,500010000,12968792826,
%T 371504434176,11649044974645,396857394156608,14596463098125000,
%U 576460752571858944,24330595941321312961,1092955779880368226560,52063675149116964615310,2621440000000512000000000
%N Number of classes of endofunctions of [n] under vertical translation mod n and reversal.
%C There are two size of classes, n or 2n.
%C n c:n c:2n (c:n)/n (c:2n)/n
%C 0 1
%C 1 1
%C 2 2
%C 3 3 3 1 1
%C 4 8 28 2 7
%C 5 25 300 5 60
%C 6 72 3852 12 642
%C 7 343 58653 49 8379
%H Andrew Howroyd, <a href="/A275551/b275551.txt">Table of n, a(n) for n = 0..100</a>
%e a(2) = 2: 11, 12.
%e a(3) = 6: 111, 112, 113, 121, 123, 131.
%e a(4) = 36: 1111, 1112, 1113, 1114, 1121, 1122, 1123, 1124, 1131, 1132, 1133, 1134, 1141, 1142, 1143, 1212, 1213, 1214, 1221, 1223, 1224, 1231, 1234, 1241, 1242, 1243, 1312, 1313, 1323, 1324, 1331, 1334, 1341, 1412, 1423, 1441.
%o (PARI) \\ see A056391 for Polya enumeration functions
%o a(n) = NonequivalentSorts(ReversiblePerms(n), CyclicPerms(n)); \\ _Andrew Howroyd_, Sep 30 2017
%Y Cf. A000312 All endofunctions
%Y Cf. A000169 Classes under translation mod n
%Y Cf. A001700 Classes under sort
%Y Cf. A056665 Classes under rotation
%Y Cf. A168658 Classes under complement to n+1
%Y Cf. A130293 Classes under translation and rotation
%Y Cf. A081721 Classes under rotation and reversal
%Y Cf. A275549 Classes under reversal
%Y Cf. A275550 Classes under reversal and complement
%Y Cf. A275552 Classes under translation and complement
%Y Cf. A275553 Classes under translation, complement and reversal
%Y Cf. A275554 Classes under translation, rotation and complement
%Y Cf. A275555 Classes under translation, rotation and reversal
%Y Cf. A275556 Classes under translation, rotation, complement and reversal
%Y Cf. A275557 Classes under rotation and complement
%Y Cf. A275558 Classes under rotation, complement and reversal
%K nonn
%O 0,3
%A _Olivier Gérard_, Aug 02 2016
%E Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017
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