login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099324 Expansion of (1+sqrt(1+4x))/(2(1+x)). 2
1, 0, -1, 3, -8, 22, -64, 196, -625, 2055, -6917, 23713, -82499, 290511, -1033411, 3707851, -13402696, 48760366, -178405156, 656043856, -2423307046, 8987427466, -33453694486, 124936258126, -467995871776, 1757900019100, -6619846420552, 24987199492704, -94520750408708 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Binomial transform is A099323. Second binomial transform is A072100.

Hankel transform is A049347. [From Paul Barry, Aug 10 2009]

LINKS

Table of n, a(n) for n=0..28.

FORMULA

a(n)=sum{k=0..2n, (2*0^(2n-k)-1)*C(k,floor(k/2))}. [From Paul Barry, Aug 10 2009]

|a(n+2)| = A091491(n+2,2). [From Philippe Deléham, Nov 25 2009]

G.f.: T(0)/(2+2*x)), where T(k) = k+2 - 2*x*(2*k+1) + 2*x*(k+2)*(2*k+3)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 27 2013

MATHEMATICA

CoefficientList[Series[(1+Sqrt[1+4x])/(2(1+x)), {x, 0, 40}], x] (* Harvey P. Dale, Jan 30 2014 *)

CROSSREFS

Cf. A014138.

Sequence in context: A047926 A192681 A014138 * A290898 A117420 A003101

Adjacent sequences:  A099321 A099322 A099323 * A099325 A099326 A099327

KEYWORD

easy,sign

AUTHOR

Paul Barry, Oct 12 2004

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 13:38 EST 2018. Contains 299581 sequences. (Running on oeis4.)