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%I #19 Sep 08 2022 08:45:13
%S 1,5,43,499,7193,123109,2430355,54229907,1347262321,36833528197,
%T 1097912385851,35409316648435,1227820993510153,45528569866101989,
%U 1797044836586213923,75200136212985945619,3324579846014080352225,154797474251689486249477,7570037033145534341015371
%N Values of Laguerre polynomials: a(n) = 2^n*n!*LaguerreL(n,-1/2,-2).
%C Not the same as the numerator of LaguerreL(n,-1/2,-2). - _Robert G. Wilson v_, Apr 08 2004
%H Alois P. Heinz, <a href="/A093620/b093620.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: exp(4*x/(1-2*x))/(1-2*x)^(1/2).
%F 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
%p a:= proc(n) option remember; `if`(n<2, 4*n+1,
%p (4*n+1)*a(n-1) -2*(n-1)*(2*n-3)*a(n-2))
%p end:
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Jun 22 2013
%t Table[2^n n!LaguerreL[n, -1/2, -2], {n, 0, 16}] (* _Robert G. Wilson v_, Apr 08 2004 *)
%o (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
%o (PARI) a(n) = 2^n*n!*pollaguerre(n, -1/2, -2); \\ _Michel Marcus_, Feb 05 2021
%o (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
%Y Bisection of A005425.
%K nonn
%O 0,2
%A _Karol A. Penson_, Apr 06 2004
%E More terms from _Robert G. Wilson v_, Apr 08 2004
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