A081669 Expansion of exp(2x)+exp(x)BesselI_0(2x).

1, 3, 7, 15, 35, 83, 205, 521, 1363, 3651, 9977, 27701, 77885, 221133, 632611, 1820375, 5262163, 15266003, 44414953, 129521141, 378427945, 1107447881, 3245329831, 9521616731, 27965113597, 82210390733, 241880335015

Offset

0,2

Comments

Binomial transform of A081668. Inverse binomial transform of A081670.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

E.g.f. exp(2x) - exp(0) + exp(x)BesselI_0(2x).

Conjecture: n*a(n) +(-6*n+5)*a(n-1) +(9*n-17)*a(n-2) +4*(n-1)*a(n-3) +12*(-n+3)*a(n-4)=0. - R. J. Mathar, Nov 24 2012

Recurrence: n*(3*n-8)*a(n) = (3*n-2)*(4*n-9)*a(n-1) - (3*n^2 - 5*n + 6)*a(n-2) - 6*(n-2)*(3*n-5)*a(n-3). - Vaclav Kotesovec, Feb 12 2014

a(n) ~ 3^(n+1/2) / (2*sqrt(Pi*n)). - Vaclav Kotesovec, Feb 12 2014

Mathematica

CoefficientList[Series[E^(2*x) - 1 + E^x*BesselI[0, 2*x], {x, 0, 20}], x]*Range[0, 20]! (* Vaclav Kotesovec, Feb 12 2014 *)

Crossrefs

Cf. A000984.

Sequence in context: A174284 A182892 A124696 * A086821 A007576 A322913

Adjacent sequences: A081666 A081667 A081668 * A081670 A081671 A081672

Keyword

easy,nonn

Author

Paul Barry, Mar 28 2003

Status

approved