A140898 Expansion of -x^2/(136*x^2+2*x-1).

0, 1, 2, 140, 552, 20144, 115360, 2970304, 21629568, 447220480, 3836062208, 68494109696, 658692679680, 10632584278016, 110847372992512, 1667726207795200, 18410695142572032, 263632154545291264, 3031118848480378880, 41916210715120369664, 496064584823572267008

Offset

1,3

Links

Table of n, a(n) for n=1..21.

Index entries for linear recurrences with constant coefficients, signature (2,136).

Formula

a(n)= ((1 + sqrt(137))^n - (1 - sqrt(137))^n) / (2*sqrt(137)).

G.f.: -x^2/(136*x^2+2*x-1). [Colin Barker, Jan 02 2013]

Mathematica

a[n_] = ((1 + Sqrt[137])^n - (1 - Sqrt[137])^n)/(2*Sqrt[137]); Table[ExpandAll[a[n]], {n, 0, 30}]
CoefficientList[Series[-x^2/(136*x^2+2*x-1), {x, 0, 30}], x] (* or *) LinearRecurrence[ {2, 136}, {0, 1}, 30] (* Harvey P. Dale, Aug 20 2019 *)

Crossrefs

Sequence in context: A101232 A093887 A152005 * A220513 A120814 A221601

Adjacent sequences: A140895 A140896 A140897 * A140899 A140900 A140901

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Jul 24 2008

Extensions

New name and more terms from Colin Barker, Jan 02 2013

Status

approved