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 A110259 Numerators in the coefficients that form the even-indexed partial quotients of the continued fraction representation of the inverse tangent of 1/x. 7
 3, 28, 704, 768, 311296, 1507328, 3145728, 130023424, 7516192768, 12884901888, 2954937499648, 12919261626368, 52776558133248, 774056185954304, 66428094503714816, 31525197391593472, 308982963234634989568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Limit a(n)/A110260(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) = A110255(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)=numerator(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. A110260 (denominators), A110255/A110256 (continued fraction), A110257/A110258. Sequence in context: A092985 A181588 A084880 * A276745 A015474 A324462 Adjacent sequences:  A110256 A110257 A110258 * A110260 A110261 A110262 KEYWORD frac,nonn AUTHOR Paul D. Hanna, Jul 18 2005 STATUS approved

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Last modified July 22 02:02 EDT 2019. Contains 325210 sequences. (Running on oeis4.)