The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A125695 Expansion of (sqrt(1+2x+9x^2)+x-1)/(2x). 3
1, 2, -2, -2, 10, -6, -42, 102, 82, -782, 814, 3854, -12454, -5014, 98694, -142218, -472158, 1932258, 19038, -14816994, 27370410, 64159962, -334154442, 121279878, 2418497010, -5523511086, -8914677362, 61259567662, -44249714438 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
First column of A125694.
Hankel transform is (-2)^C(n+1, 2)*A001045(n+2).
LINKS
FORMULA
a(n)=0^n+2*sum{k=0..floor((n-1)/2), C(n-1,2k)*C(k)*(-1)^(n-k-1)*2^k}, C(n)=A000108(n).
D-finite with recurrence: (n+1)*a(n) +(2*n-1)*a(n-1) +9*(n-2)*a(n-2)=0. - R. J. Mathar, Dec 02 2014
MATHEMATICA
CoefficientList[Series[(Sqrt[1+2x+9x^2]+x-1)/(2x), {x, 0, 30}], x] (* Harvey P. Dale, Jul 25 2013 *)
CROSSREFS
Cf. A091593.
Sequence in context: A268081 A319885 A368958 * A152681 A215603 A284563
KEYWORD
easy,sign
AUTHOR
Paul Barry, Nov 30 2006, Dec 10 2008
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 22 11:36 EDT 2024. Contains 372755 sequences. (Running on oeis4.)