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

2,2

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.

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

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 *)

Prog

(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

Crossrefs

Cf. A228340, A058307, A058279.

Sequence in context: A356142 A042793 A059272 * A378074 A289576 A370200

Adjacent sequences: A228338 A228339 A228340 * A228342 A228343 A228344

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 29 2013

Extensions

More terms from Rick L. Shepherd, Jan 22 2014

Status

approved