A274294 a(n) = 1+(n+1)^2+n!+Sum_{k=1..n-1} binomial(n,k)*n!/(n-k)!.

3, 6, 16, 50, 234, 1582, 13376, 130986, 1441810, 17572214, 234662352, 3405357826, 53334454586, 896324308830, 16083557845504, 306827170866362, 6199668952527906, 132240988644216166, 2968971263911289360, 69974827707903049554, 1727194482044146637962

Offset: 0

Author

N. J. A. Sloane, Jun 18 2016

Keywords

• nonn

Comments

Number of residuated maps on the lattice M_n.

Links

• Erika D. Foreman, Order automorphisms on the lattice of residuated maps of some special nondistributive lattices, (2015). Univ. Louisville, Electronic Theses and Dissertations. Paper 2257.

Crossrefs

Cf. A317094.

Programs

Maple

f:=n->1+(n+1)^2+n!+add(binomial(n,k)*n!/(n-k)!,k=1..n-1);
[seq(f(n),n=0..20)];

Mathematica

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 *)

Formula

a(n) = (n+1)^2 +n! + A070779(n-1), n>=1. - R. J. Mathar, Jul 16 2020