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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A243204 Expansion of 2*x/((1-sqrt(1-2*(1-sqrt(1-4*x))))*sqrt(1-2*(1-sqrt(1-4*x))) * sqrt(1-4*x)). 1
 1, 2, 8, 35, 160, 752, 3605, 17544, 86400, 429605, 2153008, 10860720, 55086421, 280692440, 1435868960, 7369703660, 37934443008, 195748568256, 1012292239955, 5244933087000, 27220980100160, 141486701601630 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA a(n) = Sum_{k=0..n} binomial(2*k-1,k)*binomial(2*n-k-1,n-k)). G.f.: A(x) = x*F'(x)/F(x), where F(x)=x*C(x)*C(x*C(x)), C(x) is g.f. of A000108. a(n) ~ 2^(4*n-3/2) / (sqrt(Pi*n) * 3^(n-1/2)). - Vaclav Kotesovec, Jun 02 2014 MATHEMATICA CoefficientList[Series[2*x / (Sqrt[1-4*x] + Sqrt[-1+2*Sqrt[1-4*x]] *Sqrt[1-4*x] + 8*x-2), {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 02 2014 *) PROG (Maxima) a(n):=sum(binomial(2*k-1, k)*binomial(2*n-k-1, n-k), k, 0, n); (PARI) x='x+O('x^50); Vec(2*x/((1-sqrt(1-2*(1-sqrt(1-4*x))))*sqrt(1-2*(1-sqrt(1-4*x)))*sqrt(1-4*x))) \\ G. C. Greubel, Jun 01 2017 CROSSREFS Cf. A000108, A121988. Sequence in context: A326294 A184786 A082759 * A279013 A137265 A364472 Adjacent sequences: A243201 A243202 A243203 * A243205 A243206 A243207 KEYWORD nonn AUTHOR Vladimir Kruchinin, Jun 01 2014 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 11 01:05 EDT 2024. Contains 375059 sequences. (Running on oeis4.)