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A093620
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Values of Laguerre polynomials: a(n) = 2^n*n!*LaguerreL(n,-1/2,-2).
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5
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1, 5, 43, 499, 7193, 123109, 2430355, 54229907, 1347262321, 36833528197, 1097912385851, 35409316648435, 1227820993510153, 45528569866101989, 1797044836586213923, 75200136212985945619, 3324579846014080352225, 154797474251689486249477, 7570037033145534341015371
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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E.g.f.: exp(4*x/(1-2*x))/(1-2*x)^(1/2).
a(n) ~ n^n*2^(n-1/2)*exp(-n+2*sqrt(2*n)-1) * (1 + 5/(6*sqrt(2*n))). - Vaclav Kotesovec, Jun 22 2013
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 4*n+1,
(4*n+1)*a(n-1) -2*(n-1)*(2*n-3)*a(n-2))
end:
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MATHEMATICA
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(4*x/(1-2*x))/(1-2*x)^(1/2))) \\ G. C. Greubel, May 11 2018
(PARI) a(n) = 2^n*n!*pollaguerre(n, -1/2, -2); \\ Michel Marcus, Feb 05 2021
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(4*x/(1-2*x))/(1-2*x)^(1/2))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 11 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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