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A317094
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a(n) = (n + 1)^2 + n!*L_n(-1), where L_n(x) is the Laguerre polynomial.
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2
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2, 6, 16, 50, 234, 1582, 13376, 130986, 1441810, 17572214, 234662352, 3405357826, 53334454586, 896324308830, 16083557845504, 306827170866362, 6199668952527906, 132240988644216166, 2968971263911289360, 69974827707903049554, 1727194482044146637962, 44552237162692939114766
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OFFSET
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0,1
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COMMENTS
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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.).
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LINKS
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FORMULA
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E.g.f.: exp(x/(1-x))/(1 - x) + exp(x)*(1 + 3*x + x^2).
a(n) ~ C*exp(2*sqrt(n)-n)*n^(n+1/4), where C = 1/sqrt(2*e). - Stefano Spezia, Jun 30 2021
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MATHEMATICA
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Table[(n+1)^2+n!*LaguerreL[n, -1], {n, 0, 21}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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