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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Wikipedia, Laguerre polynomials

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

Adjacent sequences: A160621 A160622 A160623 * A160625 A160626 A160627

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Nov 14 2009

STATUS

approved

URL: https://oeis.org/A160624

⇱ A160624 - OEIS