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A160624 Denominator of Laguerre(n, 2). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Laguerre Polynomial
FORMULA
Denominators of coefficients in expansion of exp(-2*x/(1 - x))/(1 - x). - Ilya Gutkovskiy, Aug 29 2018
EXAMPLE
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.
MAPLE
seq(denom(orthopoly[L](n, 2)), n=0 .. 100); # Robert Israel, Jul 23 2015
MATHEMATICA
Denominator[LaguerreL[Range[0, 30], 2]] (* Vincenzo Librandi, May 24 2012 *)
PROG
(PARI) for(n=0, 30, print1(denominator(sum(k=0, n, binomial(n, k)*((-2)^k/k!))), ", ")) \\ G. C. Greubel, May 06 2018
(PARI) a(n) = denominator(pollaguerre(n, 0, 2)); \\ Michel Marcus, Feb 05 2021
(Magma) [Denominator((&+[Binomial(n, k)*((-2)^k/Factorial(k)): k in [0..n]])): n in [0..30]]; // G. C. Greubel, May 06 2018
CROSSREFS
For numerators see A160623. Different from A049606.
Cf. A295382.
Sequence in context: A046983 A067655 A209430 * A049606 A046126 A143257
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Nov 14 2009
STATUS
approved

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Last modified April 14 03:44 EDT 2024. Contains 371652 sequences. (Running on oeis4.)