A226223 The number of endomorphisms of the full transformation monoid on the set {1..n}.

1, 7, 40, 345, 3226, 38503, 529614, 8219025, 141633028, 2677676931, 55021969234, 1219667932585, 28986449652564, 734758590703803, 19777243624646566, 563105619051710817, 16902630001714260832, 533291777845757001523, 17638752528002502032130, 610137644831701323189321

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..100

B. M. Schein and B. Teclezghi, Endomorphisms of finite full transformation semigroups, Proc. Amer. Math. Soc., 126 (1998) 2579-2587.

Prog

(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

Crossrefs

Cf. A000312.

Sequence in context: A121582 A239989 A356459 * A356046 A062727 A223416

Adjacent sequences: A226220 A226221 A226222 * A226224 A226225 A226226

Keyword

nonn

Author

James Mitchell, May 31 2013

Extensions

a(10)-a(20) from Charles R Greathouse IV, May 31 2013

Status

approved