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a(n) = 1+(n+1)^2+n!+Sum_{k=1..n-1} binomial(n,k)*n!/(n-k)!.
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%I #17 Feb 17 2023 15:22:07

%S 3,6,16,50,234,1582,13376,130986,1441810,17572214,234662352,

%T 3405357826,53334454586,896324308830,16083557845504,306827170866362,

%U 6199668952527906,132240988644216166,2968971263911289360,69974827707903049554,1727194482044146637962

%N a(n) = 1+(n+1)^2+n!+Sum_{k=1..n-1} binomial(n,k)*n!/(n-k)!.

%C Number of residuated maps on the lattice M_n.

%H Erika D. Foreman, <a href="http://dx.doi.org/10.18297/etd/2257">Order automorphisms on the lattice of residuated maps of some special nondistributive lattices</a>, (2015). Univ. Louisville, Electronic Theses and Dissertations. Paper 2257.

%F a(n) = (n+1)^2 +n! + A070779(n-1), n>=1. - _R. J. Mathar_, Jul 16 2020

%p f:=n->1+(n+1)^2+n!+add(binomial(n,k)*n!/(n-k)!,k=1..n-1);

%p [seq(f(n),n=0..20)];

%t Table[1+(n+1)^2+n!+Sum[Binomial[n,k] n!/(n-k)!,{k,n-1}],{n,0,20}] (* _Harvey P. Dale_, Feb 17 2023 *)

%Y Cf. A317094.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Jun 18 2016