A062197 Row sums of signed triangle A062139 (generalized a=2 Laguerre).

1, 2, 5, 14, 37, 34, -887, -14050, -168919, -1916542, -21607859, -245387858, -2799384755, -31558843486, -337767590383, -3063846770626, -11912361112367, 477367592119810, 21032925955607701, 627398853149961038, 16703816669710968821

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..448

Index entries for sequences related to Laguerre polynomials

Formula

E.g.f.: exp(-x/(1-x))/(1-x)^3.

a(n) = Sum_{m=0..n} ((-1)^m)*n!*binomial(n+2, n-m)/m!.

a(n) = 2*n*a(n-1) - (n-1)*(n+1)*a(n-2). - Vaclav Kotesovec, Aug 01 2013

a(n) = (n+2)!*hypergeom([-n],[3],1)/2. - Peter Luschny, Apr 11 2015

Maple

a := n -> (n+2)!*hypergeom([-n], [3], 1)/2:
seq(simplify(a(n)), n=0..20); # Peter Luschny, Apr 11 2015

Mathematica

Table[n!*LaguerreL[n, 2, 1], {n, 0, 20}] (* Vaclav Kotesovec, Aug 01 2013 *)

Prog

(PARI) for(n=0, 30, print1(n!*sum(k=0, n, (-1)^k*binomial(n+2, n-k)/k!), ", ")) \\ G. C. Greubel, May 13 2018
(PARI) a(n) = vecsum(Vec(n!*pollaguerre(n, 2))); \\ Michel Marcus, Feb 06 2021
(Magma) [Factorial(n)*(&+[(-1)^k*Binomial(n+2, n-k)/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, May 13 2018

Crossrefs

Cf. A062139.

Sequence in context: A363106 A005955 A186903 * A030016 A248733 A099485

Adjacent sequences: A062194 A062195 A062196 * A062198 A062199 A062200

Keyword

sign,easy

Author

Wolfdieter Lang, Jun 19 2001

Status

approved