OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..349
FORMULA
a(n) ~ n^(n+3/20)*5^n*exp(-n+2*sqrt(n)-1/2)/sqrt(2) * (1 + 643/(1200*sqrt(n))). - Vaclav Kotesovec, Jun 24 2013
From G. C. Greubel, May 13 2018: (Start)
E.g.f.: 1/(1 - 5*x)^(4/5)*exp(5*x/(1 - 5*x)).
a(n) = (10*n -1)*a(n-1) - (n-1)*(25*n - 30)*a(n-2). (End)
MAPLE
A089916 := proc(n)
5^n*n!*LaguerreL(n, -1/5, -1) ;
simplify(%) ;
end proc:
seq(A089916(n), n=0..10) ; # R. J. Mathar, Nov 12 2011
MATHEMATICA
Table[5^n*n!*LaguerreL[n, -1/5, -1], {n, 0, 20}] (* Vaclav Kotesovec, Jun 24 2013 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(1/(1 - 5*x)^(4/5)*exp(5*x/(1 - 5*x)))) \\ G. C. Greubel, May 13 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients( R!(1/(1 - 5*x)^(4/5)*Exp(5*x/(1 - 5*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 13 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Nov 14 2003
EXTENSIONS
Terms a(13) onward added by G. C. Greubel, May 13 2018
STATUS
approved