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 A275549 Number of classes of endofunctions of [n] under reversal. 15
 1, 1, 3, 18, 136, 1625, 23436, 412972, 8390656, 193739769, 5000050000, 142656721086, 4458051717120, 151437584670385, 5556003465485760, 218946946471875000, 9223372039002259456, 413620131002462320337, 19673204037747448432896, 989209827833222327690890 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS f and g are in the same class if function g(i) = f(n+1-i) for all i. Decomposition by class size . n    1      2 --------------- 1    1      0 2    2      1 3    9      9 4    16     120 5    125    1500 6    216    23220 7    2401   410571 . Demonstration for the formula: the classes are either of size 1 or 2. The classes of size 1 is for functions invariant by reversal. They are specified by half their values, including one more if n is odd. Their number is n^(ceiling(n/2)). So the number of classes under this symmetry is half (the number of functions + the number of classes of size 1). LINKS FORMULA a(n) = (n^n+n^ceiling(n/2))/2. CROSSREFS Cf. A000312 All endofunctions Cf. A000169 Classes under translation mod n Cf. A001700 Classes under sort Cf. A056665 Classes under rotation Cf. A168658 Classes under complement to n+1 Cf. A130293 Classes under translation and rotation Cf. A081721 Classes under rotation and reversal Cf. A275550 Classes under reversal and complement Cf. A275551 Classes under translation and reversal Cf. A275552 Classes under translation and complement Cf. A275553 Classes under translation, complement and reversal Cf. A275554 Classes under translation, rotation and complement Cf. A275555 Classes under translation, rotation and reversal Cf. A275556 Classes under translation, rotation, complement and reversal Cf. A275557 Classes under rotation and complement Cf. A275558 Classes under rotation, complement and reversal Cf. A078707 Endofunctions symmetric around their middle (stable by reversal). Sequence in context: A247452 A118970 A003122 * A039618 A183363 A216492 Adjacent sequences:  A275546 A275547 A275548 * A275550 A275551 A275552 KEYWORD nonn,easy AUTHOR Olivier Gérard, Aug 01 2016 STATUS approved

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Last modified January 20 16:20 EST 2019. Contains 319335 sequences. (Running on oeis4.)