The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A098469 A sequence related to the even-indexed Catalan numbers. 1
 1, 2, 6, 20, 78, 332, 1516, 7240, 35734, 180620, 929940, 4858328, 25687052, 137177016, 738819672, 4008435984, 21886788582, 120178329740, 663179894788, 3675923244856, 20456707469540, 114254175491304, 640223315385576 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A098465. Second binomial transform of (1,0,2,0,14,0,132,0,1430,...) (set odd-indexed Catalan numbers to zero). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..300 FORMULA G.f.: (sqrt(1+2*x) - sqrt(1-6*x))/(4*x*sqrt(1-2*x)). a(n) = Sum_{k=0..floor(n/2)} C(n,2k)*C(k)*2^(n-2k). a(n) = Sum_{k=0..n} C(n,k)*2^(n-k)*C(k)*(1-(-1)^k)/2. Recurrence: n*(n+1)*a(n) = 4*n*(2*n-1)*a(n-1) - 4*(2*n^2 - 4*n + 3)*a(n-2) - 16*(n-2)*(2*n-3)*a(n-3) + 48*(n-3)*(n-2)*a(n-4). - Vaclav Kotesovec, Oct 24 2012 a(n) ~ 3*6^(n+1/2)/(8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 24 2012 MATHEMATICA CoefficientList[Series[(Sqrt[1+2*x]-Sqrt[1-6*x])/(4*x*Sqrt[1-2*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 24 2012 *) PROG (PARI) x='x+O('x^66); Vec((sqrt(1+2*x)-sqrt(1-6*x))/(4*x*sqrt(1-2*x))) \\ Joerg Arndt, May 11 2013 CROSSREFS Cf. A048990. Sequence in context: A370947 A150181 A150182 * A081563 A038393 A357798 Adjacent sequences: A098466 A098467 A098468 * A098470 A098471 A098472 KEYWORD easy,nonn AUTHOR Paul Barry, Sep 09 2004, corrected Mar 31 2007 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.

Last modified August 5 21:38 EDT 2024. Contains 374956 sequences. (Running on oeis4.)