login
The number of endomorphisms of the symmetric inverse monoid on the set {1..n}.
1

%I #17 Jan 22 2020 14:40:14

%S 1,3,14,54,306,918,4524,25560,168828,1315764,11998584,125358192,

%T 1466062200,18835528104,262376016912,3927709053792,62795044663056,

%U 1067217284481840,19208039592749472,364940846656681536,7298740111856220576,153273039685710932448,3372003538678423189440

%N The number of endomorphisms of the symmetric inverse monoid on the set {1..n}.

%H James Mitchell, <a href="/A226466/b226466.txt">Table of n, a(n) for n = 0..100</a>

%H B. M. Schein and B. Teclezghi, <a href="https://doi.org/10.1006/jabr.1997.7132">Endomorphisms of finite symmetric inverse semigroups</a>, J. Algebra, 198 (1997) 300-310.

%o (PARI) a(n)=if(n==0, return (1), if(n<5, return([3, 14, 54, 306][n])));n!*(3+sum(m=0, n, sum(k=0, m\2, 2^(m-3*k)/((n-m)!*(m-2*k)!*k!))))

%Y Cf. A226223.

%K nonn

%O 0,2

%A _James Mitchell_, Jun 08 2013