A160623 Numerator of Laguerre(n, 2).

1, -1, -1, -1, 1, 11, 37, 209, 113, 23, -4381, -84389, -310517, -4103887, -25059901, -274436401, -13182829, -104362273, 1748375381, 690031209911, 4647089032189, 112233351264271, 1276100569319881, 2131681036523177, 71497025649480187, 1365106755339875117

Offset

0,6

Links

Harvey P. Dale, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Wikipedia, Laguerre polynomials

Formula

Numerators 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.

Mathematica

Numerator[LaguerreL[Range[0, 30], 2]] (* Harvey P. Dale, May 16 2012 *)

Prog

(PARI) for(n=0, 30, print1(numerator(sum(k=0, n, binomial(n, k)*((-2)^k/k!))), ", ")) \\ G. C. Greubel, May 06 2018
(Magma) [Numerator((&+[Binomial(n, k)*((-2)^k/Factorial(k)): k in [0..n]])): n in [0..30]]; // G. C. Greubel, May 06 2018

Crossrefs

For denominators see A160624.

Cf. A295382.

Sequence in context: A287018 A152094 A227412 * A147556 A201312 A120833

Adjacent sequences: A160620 A160621 A160622 * A160624 A160625 A160626

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 14 2009

Status

approved