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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<x>:=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

Clark Kimberling

STATUS

approved

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