%I #18 Sep 08 2022 08:45:12
%S 1,7,93,1747,41881,1214079,41146933,1592909707,69246230193,
%T 3336315914359,176318707191181,10135074699232707,629237102421392713,
%U 41946693027934462447,2987346130479191856741,226298375000985686615419,18164688323228843027295073
%N Special values of generalized Laguerre polynomials L_n^(alpha)(x): a(n) = 4^n *n! *L_n^(-1/4)(-1).
%C L_n^(alpha)(x) is orthogonal over the interval (0,infinity) with weight exp(-x)*x^alpha. L_1^(alpha)(x) = -x+1+alpha.
%H G. C. Greubel, <a href="/A089915/b089915.txt">Table of n, a(n) for n = 0..360</a>
%F From _Vaclav Kotesovec_, Jul 31 2013: (Start)
%F a(n) = (8*n-1)*a(n-1) - 4*(n-1)*(4*n-5)*a(n-2).
%F a(n) ~ 2^(2*n-1/2)*n^(n+1/8)*exp(2*sqrt(n)-n-1/2) * (1+97/(192*sqrt(n))).
%F (End)
%t Table[4^n*n!*LaguerreL[n, -1/4, -1], {n, 0, 20}] (* _Vaclav Kotesovec_, Jul 31 2013 *)
%t RecurrenceTable[{a[n] == (8*n-1)*a[n-1] - 4*(n-1)*(4*n-5)*a[n-2], a[0] == 1, a[1] == 7}, a, {n, 0, 50}] (* _G. C. Greubel_, May 14 2018 *)
%o (Magma) I:=[7,93]; [1] cat [n le 2 select I[n] else (8*n-1)*Self(n-1) - 4*(n-1)*(4*n-5)*Self(n-2): n in [1..30]]; // _G. C. Greubel_, May 14 2018
%o (PARI) m=30; v=concat([7,93], vector(m-2)); for(n=3, m, v[n]=(8*n-1)*v[n-1]-4*(n-1)*(4*n-5)*v[n-2]); concat([1], v) \\ _G. C. Greubel_, May 14 2018
%K nonn
%O 0,2
%A _Karol A. Penson_, Nov 14 2003