A089916 a(n) = 5^n *n! *L_n^{-1/5}(-1), where L_n^(alpha)(x) are generalized Laguerre polynomials.

1, 9, 151, 3569, 107481, 3910349, 166221991, 8067313749, 439513616881, 26531702453969, 1756401581518551, 126445101373298009, 9830454366312366601, 820512954392820339669, 73156610496742582153831, 6937257394297322500319549, 697004737436352946597046241

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

Sequence in context: A337672 A027018 A326012 * A143000 A143905 A274502

Adjacent sequences: A089913 A089914 A089915 * A089917 A089918 A089919

Keyword

nonn

Author

Karol A. Penson, Nov 14 2003

Extensions

Terms a(13) onward added by G. C. Greubel, May 13 2018

Status

approved