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A317094 a(n) = (n + 1)^2 + n!*L_n(-1), where L_n(x) is the Laguerre polynomial. 1

%I

%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 Santiago Quintero, Sergio Ramírez, 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).

%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

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Last modified June 24 21:38 EDT 2021. Contains 345433 sequences. (Running on oeis4.)