A089917 a(n) = 6^n *n! *L_n^{-1/6}(-1), where L_n^(alpha)(x) are generalized Laguerre polynomials.

1, 11, 223, 6353, 230353, 10083971, 515554831, 30085247513, 1970313094753, 142951182749243, 11372154669976831, 983705074834644641, 91883282167153578673, 9213208393354101289523, 986754808994210521840303

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..340

Formula

E.g.f.: exp(6*x/(1-6*x))/(1-6*x)^(5/6). - Vladeta Jovovic, Nov 17 2003

a(n) ~ n^(n+1/6)*2^(n-1/2)*3^n*exp(-n+2*sqrt(n)-1/2) * (1 + 5/(9*sqrt(n))). - Vaclav Kotesovec, Jun 24 2013

a(n) = (12*n -1)*a(n-1) - (n-1)*(36*n - 42)*a(n-2). - G. C. Greubel, May 13 2018

Maple

A089917 := proc(n)
        6^n*n!*LaguerreL(n, -1/6, -1) ;
        simplify(%) ;
end proc:
seq(A089917(n), n=0..10) ; # R. J. Mathar, Nov 12 2011

Mathematica

Table[6^n*n!*LaguerreL[n, -1/6, -1], {n, 0, 20}] (* Vaclav Kotesovec, Jun 24 2013 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(1/(1 - 6*x)^(5/6)*exp(6*x/(1 - 6*x)))) \\ G. C. Greubel, May 13 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients( R!(1/(1 - 6*x)^(5/6)*Exp(6*x/(1 - 6*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 13 2018

Crossrefs

Sequence in context: A103611 A142541 A295542 * A294388 A281257 A187646

Adjacent sequences: A089914 A089915 A089916 * A089918 A089919 A089920

Keyword

nonn

Author

Karol A. Penson, Nov 14 2003

Status

approved