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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
OFFSET
0,4
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
KEYWORD
cofr,easy,nonn
AUTHOR
Thomas Baruchel, Jan 18 2005
STATUS
approved