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

Author

Thomas Baruchel, Jan 18 2005

Keywords

• cofr
• easy
• nonn

Links

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

Programs

Mathematica

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

PARI

contfrac((besseli(0,1/2)/besseli(1,1/2)-1)/2)

PARI

a(n) = 2/3*n*!(n%3)+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