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%I #17 Sep 08 2022 08:45:12
%S 1,11,223,6353,230353,10083971,515554831,30085247513,1970313094753,
%T 142951182749243,11372154669976831,983705074834644641,
%U 91883282167153578673,9213208393354101289523,986754808994210521840303
%N a(n) = 6^n *n! *L_n^{-1/6}(-1), where L_n^(alpha)(x) are generalized Laguerre polynomials.
%H G. C. Greubel, <a href="/A089917/b089917.txt">Table of n, a(n) for n = 0..340</a>
%F E.g.f.: exp(6*x/(1-6*x))/(1-6*x)^(5/6). - _Vladeta Jovovic_, Nov 17 2003
%F 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
%F a(n) = (12*n -1)*a(n-1) - (n-1)*(36*n - 42)*a(n-2). - _G. C. Greubel_, May 13 2018
%p A089917 := proc(n)
%p 6^n*n!*LaguerreL(n,-1/6,-1) ;
%p simplify(%) ;
%p end proc:
%p seq(A089917(n),n=0..10) ; # _R. J. Mathar_, Nov 12 2011
%t Table[6^n*n!*LaguerreL[n,-1/6,-1],{n,0,20}] (* _Vaclav Kotesovec_, Jun 24 2013 *)
%o (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
%o (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
%K nonn
%O 0,2
%A _Karol A. Penson_, Nov 14 2003
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