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

2, 6, 16, 50, 234, 1582, 13376, 130986, 1441810, 17572214, 234662352, 3405357826, 53334454586, 896324308830, 16083557845504, 306827170866362, 6199668952527906, 132240988644216166, 2968971263911289360, 69974827707903049554, 1727194482044146637962, 44552237162692939114766

Offset: 0

Author

Stefano Spezia, Jan 08 2020

Keywords

• easy
• nonn

Comments

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.).

Links

• Stefano Spezia, Table of n, a(n) for n = 0..400
• Santiago Quintero, Sergio Ramírez, Camilo Rueda, and Frank Valencia, Counting and Computing Join- Endomorphisms in Lattices . [Research Report] LIX, Ecole polytechnique; INRIA Saclay - Ile-de-France. 2019. hal-02422624.

Crossrefs

Cf. A000142 (n!), A000290, A002720, A274294, A274295.

Programs

Mathematica

Table[(n+1)^2+n!*LaguerreL[n,-1],{n,0,21}]

PARI

my(x='x + O('x^22)); Vec(serlaplace(exp(x/(1-x))/(1 - x) + exp(x)*(1 + 3*x + x^2)))

PARI

a(n) = (n+1)^2 + n!*pollaguerre(n, 0, -1); \\ Michel Marcus, Feb 05 2021

Formula

E.g.f.: exp(x/(1-x))/(1 - x) + exp(x)*(1 + 3*x + x^2).

a(n) = A000290(n+1) + A002720(n).

a(n) ~ C*exp(2*sqrt(n)-n)*n^(n+1/4), where C = 1/sqrt(2*e). - Stefano Spezia, Jun 30 2021