%I #24 Sep 08 2022 08:45:03
%S 1,3,11,47,225,1159,6067,28419,58433,-1390645,-35514309,-636045257,
%T -10431927839,-167173905393,-2678202265885,-43236880758901,
%U -703702453254783,-11485574113211501,-185707408082199317,-2901041900411825985
%N Row sums of signed triangle A062137 (generalized Laguerre, a=3).
%H Harry J. Smith, <a href="/A062146/b062146.txt">Table of n, a(n) for n = 0..100</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)^4.
%F a(n) = sum(((-1)^m)*n!*binomial(n+3, n-m)/m!, m=0..n).
%F a(n) = (2*n+1)*a(n-1) - (n-1)*(n+2)*a(n-2). - _Vaclav Kotesovec_, Aug 01 2013
%t Table[n!*LaguerreL[n, 3, 1],{n,0,20}] (* _Vaclav Kotesovec_, Aug 01 2013 *)
%o (PARI) { f=1; for (n=0, 100, if (n>1, f*=n); a=f*binomial(n+3, n); g=1; a+=sum(m=1, n, ((-1)^m)*f*binomial(n+3, n-m)/g*=m); write("b062146.txt", n, " ", a) ) } \\ _Harry J. Smith_, Aug 02 2009
%o (PARI) my(x='x+O('x^30)); Vec(exp(-x/(1-x))/(1-x)^4) \\ _G. C. Greubel_, May 11 2018
%o (PARI) a(n) = vecsum(Vec(n!*pollaguerre(n, 3))); \\ _Michel Marcus_, Feb 06 2021
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(-x/(1-x))/(1-x)^4)); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, May 11 2018
%Y Cf. A062137.
%K sign,easy
%O 0,2
%A _Wolfdieter Lang_, Jun 19 2001