%I #13 Aug 20 2021 06:25:54
%S 1,1,6,42,456,5640,93600,1728720,38344320,948931200,26555558400,
%T 817935148800,27735629644800,1020596255078400,40642432179148800,
%U 1737890081351424000,79498734605402112000,3871319396080840704000,200017645344178421760000,10925549584125028909056000
%N a(n) = n! * (number of mapping patterns on n).
%C 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.
%H Alois P. Heinz, <a href="/A254529/b254529.txt">Table of n, a(n) for n = 0..382</a>
%H Math Overflow, <a href="http://mathoverflow.net/questions/143058/what-is-the-probability-two-random-maps-on-n-symbols-commute">What is the probability two random maps on n symbols commute?</a>, 2013.
%F a(n) = n! * A001372(n). - _Joerg Arndt_, Feb 01 2015
%Y Cf. A001372, A053529, A181162.
%K nonn,easy
%O 0,3
%A _Martin Fuller_, Feb 01 2015
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