%I #51 Jun 30 2021 19:54:58
%S 2,6,16,50,234,1582,13376,130986,1441810,17572214,234662352,
%T 3405357826,53334454586,896324308830,16083557845504,306827170866362,
%U 6199668952527906,132240988644216166,2968971263911289360,69974827707903049554,1727194482044146637962,44552237162692939114766
%N a(n) = (n + 1)^2 + n!*L_n(-1), where L_n(x) is the Laguerre polynomial.
%C For n > 2, a(n) is the number of join-endomorphisms for a nondistributive lattice of size n (see Theorem 3 in Quintero et al.).
%H Stefano Spezia, <a href="/A317094/b317094.txt">Table of n, a(n) for n = 0..400</a>
%H Santiago Quintero, Sergio RamÃrez, Camilo Rueda, and Frank Valencia, <a href="https://hal.archives-ouvertes.fr/hal-02422624">Counting and Computing Join- Endomorphisms in Lattices </a>. [Research Report] LIX, Ecole polytechnique; INRIA Saclay - Ile-de-France. 2019. hal-02422624.
%F E.g.f.: exp(x/(1-x))/(1 - x) + exp(x)*(1 + 3*x + x^2).
%F a(n) = A000290(n+1) + A002720(n).
%F a(n) ~ C*exp(2*sqrt(n)-n)*n^(n+1/4), where C = 1/sqrt(2*e). - _Stefano Spezia_, Jun 30 2021
%t Table[(n+1)^2+n!*LaguerreL[n,-1],{n,0,21}]
%o (PARI) my(x='x + O('x^22)); Vec(serlaplace(exp(x/(1-x))/(1 - x) + exp(x)*(1 + 3*x + x^2)))
%o (PARI) a(n) = (n+1)^2 + n!*pollaguerre(n, 0, -1); \\ _Michel Marcus_, Feb 05 2021
%Y Cf. A000142 (n!), A000290, A002720, A274294, A274295.
%K easy,nonn
%O 0,1
%A _Stefano Spezia_, Jan 08 2020