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Denominator of Laguerre(n, -2).
3

%I #18 Sep 08 2022 08:45:45

%S 1,1,1,3,1,15,45,105,315,405,4725,155925,467775,96525,42567525,

%T 638512875,30405375,10854718875,97692469875,618718975875,189403768125,

%U 194896477400625,238206805711875,7044115540336875,8701554491004375

%N Denominator of Laguerre(n, -2).

%H Matthew House, <a href="/A160616/b160616.txt">Table of n, a(n) for n = 0..506</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>.

%F Denominators of coefficients in expansion of exp(2*x/(1 - x))/(1 - x). - _Ilya Gutkovskiy_, Aug 29 2018

%e 1, 3, 7, 43/3, 27, 719/15, 3661/45, 13991/105, 66769/315, 133261/405, 2363513/4725, 116441047/155925, ...

%t Denominator[Table[LaguerreL[n, -2], {n, 0, 50}]] (* _G. C. Greubel_, May 06 2018 *)

%o (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n, k)*(-2)^k/k!); \\ _Michel Marcus_, Aug 10 2015

%o (Magma) [Denominator((&+[Binomial(n,k)*(2^k/Factorial(k)): k in [0..n]])): n in [0..30]]; // _G. C. Greubel_, May 06 2018

%Y For numerators see A160615.

%Y Cf. A087912.

%K nonn,frac

%O 0,4

%A _N. J. A. Sloane_, Nov 14 2009