A228341 Third diagonal (T(n,2)) of triangle in A228340.

1, 2, 9, 47, 291, 2084, 16963, 154751, 1564473, 17363954, 209931921, 2746478927, 38660636899, 582656032412, 9361157155491, 159722327675759, 2884363055319153, 54962620378739666, 1102136770630112473, 23199834803611101599

Offset: 2

Author

N. J. A. Sloane, Aug 29 2013

Keywords

• nonn
• easy

Links

• Rick L. Shepherd, Table of n, a(n) for n = 2..200
• C. Cannings, The Stationary Distributions of a Class of Markov Chains, Applied Mathematics, Vol. 4 No. 5, 2013, pp. 769-773.

Crossrefs

Cf. A228340, A058307, A058279.

Programs

Mathematica

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 *)

PARI

v = [1, 2]; for(n=4, 21, v = concat(v, n*v[n-2] + v[n-3])); v \\ Rick L. Shepherd, Jan 22 2014

Formula

a(2) = 1, a(3) = 2; thereafter, a(n) = n*a(n-1) + a(n-2).

a(n) ~ c * n!, where c = BesselI(2,2)-BesselI(3,2) = 0.47620848845888... - Vaclav Kotesovec, Feb 14 2014

Extensions

More terms from Rick L. Shepherd, Jan 22 2014