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

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..448
• Index entries for sequences related to Laguerre polynomials

Crossrefs

Cf. A062139.

Programs

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

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 *)

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

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