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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, 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 19:37 EDT 2022. Contains 357063 sequences. (Running on oeis4.)