This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A026726 a(n) = T(2n,n), T given by A026725. 10
 1, 2, 7, 27, 108, 440, 1812, 7514, 31307, 130883, 548547, 2303413, 9686617, 40783083, 171868037, 724837891, 3058850316, 12915186640, 54554594416, 230526280814, 974414815782, 4119854160332, 17422801069670, 73695109608352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5. FORMULA From Philippe Deléham, Feb 11 2009: (Start) a(n) = Sum_{k=0..n} A039599(n,k)*A000045(k+1). a(n) = Sum_{k=0..n} A106566(n,k)*A122367(k). (End) From Philippe Deléham, Feb 02 2014: (Start) a(n) = Sum_{k=0..n} A236843(n+k,2*k). a(n) = Sum_{k=0..n} A236830(n,k). a(n) = A236830(n+1,1). a(n) = A165407(3*n). G.f.: C(x)/(1-x*C(x)^3), C(x) the g.f. of A000108. (End) MATHEMATICA CoefficientList[Series[4*x*(1-Sqrt[1-4*x])/(8*x^2-(1-Sqrt[1-4*x])^3), {x, 0, 30}], x] (* G. C. Greubel, Jul 16 2019 *) PROG (PARI) my(x='x+O('x^30)); Vec(4*x*(1-sqrt(1-4*x))/(8*x^2-(1-sqrt(1-4*x))^3)) \\ G. C. Greubel, Jul 16 2019 (MAGMA) R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 4*x*(1-Sqrt(1-4*x))/(8*x^2-(1-Sqrt(1-4*x))^3) )); // G. C. Greubel, Jul 16 2019 (Sage) (4*x*(1-sqrt(1-4*x))/(8*x^2-(1-sqrt(1-4*x))^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jul 16 2019 (GAP) List([0..30], n-> Sum([0..n], k-> (2*k+1)*Binomial(2*n, n-k)* Fibonacci(k+1)/(n+k+1) )); # G. C. Greubel, Jul 16 2019 CROSSREFS Cf. A000045, A000108, A026725. Sequence in context: A150594 A150595 A150596 * A150597 A150598 A026759 Adjacent sequences:  A026723 A026724 A026725 * A026727 A026728 A026729 KEYWORD nonn AUTHOR 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 20 02:08 EDT 2019. Contains 328244 sequences. (Running on oeis4.)