A098664 Expansion of e.g.f. BesselI(0,4*x)+BesselI(1,4*x)/2.

1, 1, 8, 12, 96, 160, 1280, 2240, 17920, 32256, 258048, 473088, 3784704, 7028736, 56229888, 105431040, 843448320, 1593180160, 12745441280, 24216338432, 193730707456, 369849532416, 2958796259328, 5671026163712, 45368209309696, 87246556364800, 697972450918400

Offset

0,3

Comments

Fifth binomial transform is A098665.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

G.f.: (1+8*x-sqrt(1-16*x^2))/(8*x*sqrt(1-16*x^2)).

a(n) = binomial(n, floor(n/2))*4^floor(n/2).

Conjecture: (n+1)*a(n) + 8*(n-1)*a(n-1) - 16*n*a(n-2) + 128*(2-n)*a(n-3) = 0. - R. J. Mathar, Dec 08 2011

From Amiram Eldar, Nov 10 2025: (Start)

Sum_{n>=0} 1/a(n) = 8/5 + (16/5)*sqrt(3/5)*arccosec(4).

Sum_{n>=0} (-1)^n/a(n) = 8/15 - 112*arccosec(4)/(15*sqrt(15)). (End)

Mathematica

With[{nn=30}, CoefficientList[Series[BesselI[0, 4x]+BesselI[1, 4x]/2, {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, May 14 2012 *)

Crossrefs

Cf. A098665, A195621.

Sequence in context: A147764 A226259 A162466 * A266800 A230545 A180922

Adjacent sequences: A098661 A098662 A098663 * A098665 A098666 A098667

Keyword

easy,nonn

Author

Paul Barry, Sep 20 2004

Status

approved