OFFSET
0,2
LINKS
FORMULA
E.g.f.: exp(-x/(1-x))/(1-x)^5.
a(n) = Sum_{m=0..n} (-1)^m*n!*binomial(n+5, n-m)/m!.
MATHEMATICA
Table[n!*LaguerreL[n, 5, 1], {n, 0, 20}] (* Vaclav Kotesovec, Feb 25 2014 *)
PROG
(PARI) { f=1; for (n=0, 100, if (n>1, f*=n); a=f*binomial(n+5, n); g=1; a+=sum(m=1, n, ((-1)^m)*f*binomial(n+5, n-m)/g*=m); write("b062191.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 02 2009
(PARI) my(x = 'x + O('x^30)); Vec(serlaplace(exp(-x/(1-x))/(1-x)^5)) \\ G. C. Greubel, May 11 2018
(PARI) a(n) = vecsum(Vec(n!*pollaguerre(n, 5))); \\ Michel Marcus, Feb 06 2021
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(-x/(1-x))/(1-x)^5)); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 11 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Jun 19 2001
EXTENSIONS
Typo in first formula corrected by Vaclav Kotesovec, Feb 25 2014
STATUS
approved