A101443 Continued fraction expansion of (I_0(1/2)/I_1(1/2)-1)/2 = 1.56185896... (where I_n is the modified Bessel function of the first kind).

1, 1, 1, 3, 1, 1, 5, 1, 1, 7, 1, 1, 9, 1, 1, 11, 1, 1, 13, 1, 1, 15, 1, 1, 17, 1, 1, 19, 1, 1, 21, 1, 1, 23, 1, 1, 25, 1, 1, 27, 1, 1, 29, 1, 1, 31, 1, 1, 33, 1, 1, 35, 1, 1, 37, 1, 1, 39, 1, 1, 41, 1, 1, 43, 1, 1, 45, 1, 1, 47, 1, 1, 49, 1, 1, 51, 1, 1, 53, 1, 1, 55, 1, 1, 57, 1, 1, 59, 1, 1, 61, 1

Offset

0,4

Links

Table of n, a(n) for n=0..91.

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Formula

G.f.: 1 + x*U(0) where U(k)= 1 + x/(1 - x*(2*k+2)/(1+x*(2*k+2) - 1/((2*k+2) + 1 - (2*k+2)*x/(x + 1/U(k+1))))) ; (continued fraction, 5-step). - Sergei N. Gladkovskii, Oct 07 2012

Mathematica

LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 1, 1, 3, 1, 1}, 92] (* Georg Fischer, Feb 25 2022 *)

Prog

(PARI) /* first version */ contfrac((besseli(0, 1/2)/besseli(1, 1/2)-1)/2)[n+1] /* alternate version */ 2/3*n*!(n%3)+1

Crossrefs

Sequence in context: A016562 A087501 A294951 * A228037 A184726 A046230

Adjacent sequences: A101440 A101441 A101442 * A101444 A101445 A101446

Keyword

cofr,easy,nonn

Author

Thomas Baruchel, Jan 18 2005

Status

approved