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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).

%I A254569 #6 Feb 01 2015 15:14:01
%S A254569 1,7,84,1540,37345,1145376,42402871,1849021504,93217426857,
%T A254569 5363120671120,348669188664511,25418305492373520,2064813985107357445,
%U A254569 185896884170249831320,18459391640792004885375,2012607682674617326564096,239898601216105901349115537,31132586664410794285693925664,4380971763246528510240944123071,665896706682993760478978112600400
%N 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).
%F A254569 a(n) = (A181162(n) - n^n)/2 + n^n.
%e A254569 The a(2) = 7 pairs of maps [2] -> [2] are:
%e A254569 01:  [ 1 1 ]  [ 1 1 ]
%e A254569 02:  [ 1 1 ]  [ 1 2 ]
%e A254569 03:  [ 1 2 ]  [ 1 2 ]
%e A254569 04:  [ 1 2 ]  [ 2 1 ]
%e A254569 05:  [ 1 2 ]  [ 2 2 ]
%e A254569 06:  [ 2 1 ]  [ 2 1 ]
%e A254569 07:  [ 2 2 ]  [ 2 2 ]
%Y A254569 Cf. A181162 (ordered pairs), A254570 (unordered pairs, f and g distinct).
%K A254569 nonn
%O A254569 1,2
%A A254569 _Joerg Arndt_, Feb 01 2015