A160624 Denominator of Laguerre(n, 2).
1, 1, 1, 3, 3, 15, 45, 315, 315, 2835, 14175, 155925, 467775, 6081075, 42567525, 638512875, 58046625, 10854718875, 8881133625, 1856156927625, 9280784638125, 194896477400625, 2143861251406875, 3792985290950625, 147926426347074375
Offset: 0
Examples
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.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Eric Weisstein's World of Mathematics, Laguerre Polynomial
- Wikipedia, Laguerre polynomials
Programs
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Magma
[Denominator((&+[Binomial(n,k)*((-2)^k/Factorial(k)): k in [0..n]])): n in [0..30]]; // G. C. Greubel, May 06 2018
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Maple
seq(denom(orthopoly[L](n,2)), n=0 .. 100); # Robert Israel, Jul 23 2015
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Mathematica
Denominator[LaguerreL[Range[0,30],2]] (* Vincenzo Librandi, May 24 2012 *)
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PARI
for(n=0,30, print1(denominator(sum(k=0,n, binomial(n,k)*((-2)^k/k!))), ", ")) \\ G. C. Greubel, May 06 2018
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PARI
a(n) = denominator(pollaguerre(n, 0, 2)); \\ Michel Marcus, Feb 05 2021
Formula
Denominators of coefficients in expansion of exp(-2*x/(1 - x))/(1 - x). - Ilya Gutkovskiy, Aug 29 2018