Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #28 Sep 08 2022 08:45:03
%S 1,2,5,14,37,34,-887,-14050,-168919,-1916542,-21607859,-245387858,
%T -2799384755,-31558843486,-337767590383,-3063846770626,
%U -11912361112367,477367592119810,21032925955607701,627398853149961038,16703816669710968821
%N Row sums of signed triangle A062139 (generalized a=2 Laguerre).
%H G. C. Greubel, <a href="/A062197/b062197.txt">Table of n, a(n) for n = 0..448</a>
%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F E.g.f.: exp(-x/(1-x))/(1-x)^3.
%F a(n) = Sum_{m=0..n} ((-1)^m)*n!*binomial(n+2, n-m)/m!.
%F a(n) = 2*n*a(n-1) - (n-1)*(n+1)*a(n-2). - _Vaclav Kotesovec_, Aug 01 2013
%F a(n) = (n+2)!*hypergeom([-n],[3],1)/2. - _Peter Luschny_, Apr 11 2015
%p a := n -> (n+2)!*hypergeom([-n],[3],1)/2:
%p seq(simplify(a(n)), n=0..20); # _Peter Luschny_, Apr 11 2015
%t Table[n!*LaguerreL[n, 2, 1],{n,0,20}] (* _Vaclav Kotesovec_, Aug 01 2013 *)
%o (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
%o (PARI) a(n) = vecsum(Vec(n!*pollaguerre(n, 2))); \\ _Michel Marcus_, Feb 06 2021
%o (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
%Y Cf. A062139.
%K sign,easy
%O 0,2
%A _Wolfdieter Lang_, Jun 19 2001