A095159 Numerator of b(n) given by b(1) = 1, b(2) = 2; for n >= 3, b(n) = (-1)^n (2n-1) ((n-2)!!)^2/((n-1)!!)^2, where n!! is the double factorial A006882.

1, 2, -5, 28, -81, 704, -325, 768, -20825, 311296, -83349, 1507328, -1334025, 3145728, -5337189, 130023424, -1366504425, 7516192768, -5466528925, 12884901888, -87470372561, 2954937499648, -349899121845, 12919261626368, -22394407746529, 52776558133248, -89580335298125

Offset

1,2

Comments

b(n) is such that the continued fraction [b(1); b(2), b(3),..., b(n)] is equal to sum{k=1 to n} 1/k = H(n) = the n-th harmonic number, for all positive integers n.

a(2n)/A095175(2n) -> pi as n -> inf.; a(2n+1)/A095175(2n+1) -> -4/pi as n -> inf. - Leroy Quet, Aug 03 2004

Links

Table of n, a(n) for n=1..27.

Example

1, 2, -5/4, 28/9, -81/64, 704/225, -325/256, 768/245, -20825/16384, 311296/99225, ...

Crossrefs

Cf. A006882, A095175.

Sequence in context: A151775 A286879 A326230 * A047132 A364112 A264699

Adjacent sequences: A095156 A095157 A095158 * A095160 A095161 A095162

Keyword

sign,frac

Author

N. J. A. Sloane, based on a suggestion of Leroy Quet, Jul 03 2004

Status

approved