A254529 a(n) = n! * (number of mapping patterns on n).

1, 1, 6, 42, 456, 5640, 93600, 1728720, 38344320, 948931200, 26555558400, 817935148800, 27735629644800, 1020596255078400, 40642432179148800, 1737890081351424000, 79498734605402112000, 3871319396080840704000, 200017645344178421760000, 10925549584125028909056000

Offset: 0

Author

Martin Fuller, Feb 01 2015

Keywords

• nonn
• easy

Comments

a(n) is the number of ordered pairs (p, f) such that p f = f p, where p is a permutation and f is an endofunction.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..382
• Math Overflow, What is the probability two random maps on n symbols commute?, 2013.

Crossrefs

Cf. A001372, A053529, A181162.

Formula

a(n) = n! * A001372(n). - Joerg Arndt, Feb 01 2015