A049346 Coefficient of x^(-n) in expansion of continued fraction 0, x, x^2, x^3, x^4, ... .

0, 1, 0, 0, -1, 0, 0, 1, 0, 1, -1, 0, -2, 1, -1, 3, -2, 3, -4, 4, -6, 7, -8, 11, -13, 16, -20, 24, -31, 37, -46, 58, -70, 88, -108, 133, -167, 204, -252, 315, -386, 479, -594, 731, -909, 1122, -1386, 1720, -2124, 2628, -3254, 4022, -4980, 6160, -7618, 9432, -11665, 14433, -17860, 22093, -27341, 33824, -41847

Offset: 0

Author

Alain Lasjauniasith (lasjauni(AT)math.u-bordeaux.fr.yyy.com)

Keywords

• sign

Comments

Absolute values are essentially A227310. - Franklin T. Adams-Watters, Oct 31 2014

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

G.f.: 1 - 1/G(0), where G(k)= 1 + x^(k+1)/(1 - x^(k+1)/G(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Jun 29 2013

G.f.: W(0) - 1, where W(k) = 1 - x^(k+1)/( x^(k+1) - 1/(1 - x^(k+1)/( x^(k+1) + 1/W(k+1) ))); (continued fraction). - Sergei N. Gladkovskii, Aug 27 2013

Extensions

Added more terms, Joerg Arndt, Jun 29 2013