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, 7, 84, 1540, 37345, 1145376, 42402871, 1849021504, 93217426857, 5363120671120, 348669188664511, 25418305492373520, 2064813985107357445, 185896884170249831320, 18459391640792004885375, 2012607682674617326564096, 239898601216105901349115537, 31132586664410794285693925664, 4380971763246528510240944123071, 665896706682993760478978112600400

Offset: 1

Author

Joerg Arndt, Feb 01 2015

Keywords

• nonn

Examples

			The a(2) = 7 pairs of maps [2] -> [2] are:
01:  [ 1 1 ]  [ 1 1 ]
02:  [ 1 1 ]  [ 1 2 ]
03:  [ 1 2 ]  [ 1 2 ]
04:  [ 1 2 ]  [ 2 1 ]
05:  [ 1 2 ]  [ 2 2 ]
06:  [ 2 1 ]  [ 2 1 ]
07:  [ 2 2 ]  [ 2 2 ]
		

Crossrefs

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

Formula

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