This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A110260 Denominators in the coefficients that form the even-indexed partial quotients of the continued fraction representation of the inverse tangent of 1/x. 7
 1, 9, 225, 245, 99225, 480249, 1002001, 41409225, 2393453205, 4102737925, 940839860961, 4113258565689, 16802526820625, 246430431820125, 21147754404155625, 10036045423404225, 98363281194784809225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Limit A110259(n)/a(n) = limit A110255(2*n)/A110256(2*n) = Pi. LINKS Paul D. Hanna, Table of n, a(n) for n = 1..200 FORMULA a(n) = A110256(2*n). EXAMPLE arctan(1/x) = 1/x - 1/(3*x^3) + 1/(5*x^5) - 1/(7*x^7) +-... = [0; x, 3*x, 5/4*x, 28/9*x, 81/64*x, 704/225*x, 325/256*x, 768/245*x, 20825/16384*x, 311296/99225*x, 83349/65536*x, 1507328/480249*x, 1334025/1048576*x, 3145728/1002001*x,...] = 1/(x + 1/(3*x + 1/(5/4*x + 1/(28/9*x + 1/(81/64*x +...))))). The coefficients of x in the even-indexed partial quotients converge to Pi: {3, 28/9, 704/225, 768/245, 311296/99225, ...}. The coefficients of x in the odd-indexed partial quotients converge to 4/Pi: {1, 5/4, 81/64, 325/256, 20825/16384, ...}. PROG (PARI) {a(n)=denominator(subst((contfrac( sum(k=0, 2*n+2, (-1)^k/x^(2*k+1)/(2*k+1)), 2*n+2))[2*n+1], x, 1))} CROSSREFS Cf. A110259 (numerators), A110255/A110256 (continued fraction), A110257/A110258. Sequence in context: A205568 A264848 A033632 * A036896 A120319 A057530 Adjacent sequences:  A110257 A110258 A110259 * A110261 A110262 A110263 KEYWORD frac,nonn AUTHOR Paul D. Hanna, Jul 18 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 25 14:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)