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A160624 Denominator of Laguerre(n, 2).

%I A160624 #25 Feb 16 2025 08:33:10
%S A160624 1,1,1,3,3,15,45,315,315,2835,14175,155925,467775,6081075,42567525,
%T A160624 638512875,58046625,10854718875,8881133625,1856156927625,
%U A160624 9280784638125,194896477400625,2143861251406875,3792985290950625,147926426347074375
%N A160624 Denominator of Laguerre(n, 2).
%H A160624 Vincenzo Librandi, <a href="/A160624/b160624.txt">Table of n, a(n) for n = 0..200</a>
%H A160624 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>
%H A160624 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%F A160624 Denominators of coefficients in expansion of exp(-2*x/(1 - x))/(1 - x). - _Ilya Gutkovskiy_, Aug 29 2018
%e A160624 1, -1, -1, -1/3, 1/3, 11/15, 37/45, 209/315, 113/315, 23/2835, -4381/14175, -84389/155925, -310517/467775, ... = A160623/A160624.
%p A160624 seq(denom(orthopoly[L](n,2)), n=0 .. 100); # _Robert Israel_, Jul 23 2015
%t A160624 Denominator[LaguerreL[Range[0,30],2]] (* _Vincenzo Librandi_, May 24 2012 *)
%o A160624 (PARI) for(n=0,30, print1(denominator(sum(k=0,n, binomial(n,k)*((-2)^k/k!))), ", ")) \\ _G. C. Greubel_, May 06 2018
%o A160624 (PARI) a(n) = denominator(pollaguerre(n, 0, 2)); \\ _Michel Marcus_, Feb 05 2021
%o A160624 (Magma) [Denominator((&+[Binomial(n,k)*((-2)^k/Factorial(k)): k in [0..n]])): n in [0..30]]; // _G. C. Greubel_, May 06 2018
%Y A160624 For numerators see A160623. Different from A049606.
%Y A160624 Cf. A295382.
%K A160624 nonn,frac
%O A160624 0,4
%A A160624 _N. J. A. Sloane_, Nov 14 2009