A142155 Expansion of x/( 1+x-x^2-x^4-x^5-x^6-x^7+x^9+x^10 ).

1, -1, 2, -3, 6, -9, 17, -27, 48, -80, 139, -233, 402, -680, 1165, -1979, 3382, -5754, 9822, -16727, 28531, -48613, 82893, -141268, 240847, -410505, 699808, -1192838, 2033410, -3466085, 5908459, -10071512, 17168221, -29265017, 49885842, -85035890, 144953845, -247090156, 421194210

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 15 2008

Keywords

• sign
• easy

Comments

limit_{n->infinity} a(n+1)/a(n) = -1.70461...

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,1,0,1,1,1,1,0,-1,-1).
• E. W. Weisstein, Polylogarithm, MathWorld (see the remark concerning Li_17).

Crossrefs

Cf. A073011.

Programs

Mathematica

Rest[CoefficientList[Series[x/(1+x-x^2-x^4-x^5-x^6-x^7+x^9+x^10),{x,0,50}],x]]  (* Harvey P. Dale, Mar 03 2011 *)

PARI

x='x+O('x^50); Vec(x/(1+x-x^2-x^4-x^5-x^6-x^7+x^9+x^10)) \\ G. C. Greubel, Mar 05 2017

Formula

Generating function g(x) = x/( 1+x-x^2-x^4-x^5-x^6-x^7+x^9+x^10 ) = 1/(x^10* p(1/x)) with p(x)= 1 +x -x^3 -x^4 -x^5 -x^6 -x^8 +x^9 +x^10.

Extensions

Definition simplified by the Assoc. Eds. of the OEIS, Jun 30 2010