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 A254569 The number of unordered pairs (f,g) of functions from {1..n} to itself such that fg=gf (i.e., f(g(i))=g(f(i)) for all i). 1

%I

%S 1,7,84,1540,37345,1145376,42402871,1849021504,93217426857,

%T 5363120671120,348669188664511,25418305492373520,2064813985107357445,

%U 185896884170249831320,18459391640792004885375,2012607682674617326564096,239898601216105901349115537,31132586664410794285693925664,4380971763246528510240944123071,665896706682993760478978112600400

%N The number of unordered pairs (f,g) of functions from {1..n} to itself such that fg=gf (i.e., f(g(i))=g(f(i)) for all i).

%F a(n) = (A181162(n) - n^n)/2 + n^n.

%e The a(2) = 7 pairs of maps [2] -> [2] are:

%e 01: [ 1 1 ] [ 1 1 ]

%e 02: [ 1 1 ] [ 1 2 ]

%e 03: [ 1 2 ] [ 1 2 ]

%e 04: [ 1 2 ] [ 2 1 ]

%e 05: [ 1 2 ] [ 2 2 ]

%e 06: [ 2 1 ] [ 2 1 ]

%e 07: [ 2 2 ] [ 2 2 ]

%Y Cf. A181162 (ordered pairs), A254570 (unordered pairs, f and g distinct).

%K nonn

%O 1,2

%A _Joerg Arndt_, Feb 01 2015

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Last modified March 21 17:39 EDT 2023. Contains 361408 sequences. (Running on oeis4.)