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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) where f and g are distinct.
2

%I #5 Feb 01 2015 15:14:18

%S 0,3,57,1284,34220,1098720,41579328,1832244288,92830006368,

%T 5353120671120,348383876993900,25409389391925264,2064511110000765192,

%U 185885772163424273304,18458953746901624026000,2012589235930543617012480,239897773975844015012351360,31132547318002718989156350240,4380969784826872849927354999092,665896601825393760478978112600400

%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) where f and g are distinct.

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

%e The a(2) = 3 pairs of maps [2] -> [2] are:

%e 01: [ 1 1 ] [ 1 2 ]

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

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

%Y Cf. A181162 (ordered pairs), A254569 (unordered pairs).

%K nonn

%O 1,2

%A _Joerg Arndt_, Feb 01 2015