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%I #15 Sep 30 2017 23:49:42
%S 1,1,2,10,72,819,11772,206572,4196352,96871525,2500050000,71328400806,
%T 2229026605056,75718793541895,2778001759096256,109473473278652344,
%U 4611686020574871552,206810065502975099529
%N Number of classes of endofunctions of [n] under reversal and complement to n+1.
%C Possible classes size are 1,2,4
%C n 1 2 4
%C -----------------
%C 1 1 0 0
%C 2 0 2 0
%C 3 1 5 4
%C 4 0 16 56
%C 5 1 74 744
%C 6 0 216 11556
%C 7 1 1371 205200.
%C Classes of size 2 can be further decomposed by whether the function is stable by reversal or stable by (reversal and complement).
%C n 2 2-r 2-rc
%C -----------------
%C 1 0 0 0
%C 2 2 1 1
%C 3 5 4 1
%C 4 16 8 8
%C 5 74 62 12
%C 6 216 108 108
%C 7 1371 1200 171.
%H Andrew Howroyd, <a href="/A275550/b275550.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = (1+(-1)^(n+1)+2*n^n+(3+((-1)^(n+1))*(n-1)+n)*n^(floor(n/2)) )/8.
%F Classes of size 2: (2 (-1 + (-1)^n) + n^floor(n/2)*(3 + ((-1)^(1 + n))* (-1 + n) + n))/4.
%t Table[1/8 (1+(-1)^(1+n)+2 n^n+n^Floor[n/2] (3+(-1)^(n+1) (-1+n)+n)),{n,1,17}]
%o (PARI) a(n) = (1+(-1)^(n+1)+2*n^n+(3+((-1)^(n+1))*(n-1)+n)*n^(floor(n/2)) )/8; \\ _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. A275551 Classes under translation and reversal
%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
%Y Cf. A192396 floor(((k+1)^n-(1+(-1)^k)/2)/2)
%Y Cf. A275574 (2-r classes)
%K nonn,easy
%O 0,3
%A _Olivier Gérard_, Aug 01 2016
%E Duplicate a(7) removed by _Andrew Howroyd_, Sep 30 2017
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