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%I #18 Jun 08 2013 13:12:24
%S 1,7,40,345,3226,38503,529614,8219025,141633028,2677676931,
%T 55021969234,1219667932585,28986449652564,734758590703803,
%U 19777243624646566,563105619051710817,16902630001714260832,533291777845757001523,17638752528002502032130,610137644831701323189321
%N The number of endomorphisms of the full transformation monoid on the set {1..n}.
%H Charles R Greathouse IV, <a href="/A226223/b226223.txt">Table of n, a(n) for n = 1..100</a>
%H B. M. Schein and B. Teclezghi, <a href="http://www.ams.org/journals/proc/1998-126-09/S0002-9939-98-04764-9/S0002-9939-98-04764-9.pdf">Endomorphisms of finite full transformation semigroups</a>, Proc. Amer. Math. Soc., 126 (1998) 2579-2587.
%o (PARI) a(n)=if(n<5,return([1, 7, 40, 345][n]));n!*(sum(m=1,n,m^(n-m)*sum(k=0,(m-1)\2,sum(r=1,m-2*k,r^(m-k-r)/(m-2*k-r)!/r!)/2^k/k!)/(n-m)!)+1) \\ _Charles R Greathouse IV_, May 31 2013
%Y Cf. A000312.
%K nonn
%O 1,2
%A _James Mitchell_, May 31 2013
%E a(10)-a(20) from _Charles R Greathouse IV_, May 31 2013