%I #16 Feb 14 2014 10:36:06
%S 1,2,9,47,291,2084,16963,154751,1564473,17363954,209931921,2746478927,
%T 38660636899,582656032412,9361157155491,159722327675759,
%U 2884363055319153,54962620378739666,1102136770630112473,23199834803611101599
%N Third diagonal (T(n,2)) of triangle in A228340.
%H Rick L. Shepherd, <a href="/A228341/b228341.txt">Table of n, a(n) for n = 2..200</a>
%H C. Cannings, <a href="http://dx.doi.org/10.4236/am.2013.45105">The Stationary Distributions of a Class of Markov Chains</a>, Applied Mathematics, Vol. 4 No. 5, 2013, pp. 769-773.
%F a(2) = 1, a(3) = 2; thereafter, a(n) = n*a(n-1) + a(n-2).
%F a(n) ~ c * n!, where c = BesselI(2,2)-BesselI(3,2) = 0.47620848845888... - _Vaclav Kotesovec_, Feb 14 2014
%t Table[FullSimplify[-2*BesselI[1+n,-2] * (BesselK[2,2] + BesselK[3,2]) + 2*(BesselI[2,2] - BesselI[3,2]) * BesselK[1+n,2]],{n,2,20}] (* _Vaclav Kotesovec_, Feb 14 2014 *)
%o (PARI)
%o v = [1, 2]; for(n=4, 21, v = concat(v, n*v[n-2] + v[n-3])); v \\ _Rick L. Shepherd_, Jan 22 2014
%Y Cf. A228340, A058307, A058279.
%K nonn,easy
%O 2,2
%A _N. J. A. Sloane_, Aug 29 2013
%E More terms from _Rick L. Shepherd_, Jan 22 2014