A254570 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.

0, 3, 57, 1284, 34220, 1098720, 41579328, 1832244288, 92830006368, 5353120671120, 348383876993900, 25409389391925264, 2064511110000765192, 185885772163424273304, 18458953746901624026000, 2012589235930543617012480, 239897773975844015012351360, 31132547318002718989156350240, 4380969784826872849927354999092, 665896601825393760478978112600400

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

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

Example

The a(2) = 3 pairs of maps [2] -> [2] are:
01:  [ 1 1 ]  [ 1 2 ]
02:  [ 1 2 ]  [ 2 1 ]
03:  [ 1 2 ]  [ 2 2 ]

Crossrefs

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

Sequence in context: A157929 A053725 A053774 * A308404 A009723 A069992

Adjacent sequences: A254567 A254568 A254569 * A254571 A254572 A254573

Keyword

nonn

Author

Joerg Arndt, Feb 01 2015

Status

approved