A026726 a(n) = T(2n,n), T given by A026725.

1, 2, 7, 27, 108, 440, 1812, 7514, 31307, 130883, 548547, 2303413, 9686617, 40783083, 171868037, 724837891, 3058850316, 12915186640, 54554594416, 230526280814, 974414815782, 4119854160332, 17422801069670, 73695109608352, 311768697325788, 1319136935150530

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)

n*(5*n-11)*a(n) +2*(-20*n^2+59*n-30)*a(n-1) +15*(5*n^2-19*n+16)*a(n-2) +2*(5*n-6)*(2*n-5)*a(n-3)=0. - R. J. Mathar, Oct 26 2019

n*a(n) +(-7*n+4)*a(n-1) +(7*n-2)*a(n-2) +(19*n-60)*a(n-3) +2*(2*n-7)*a(n-4)=0. - R. J. Mathar, Oct 26 2019

Maple

A026726 := proc(n)
    A026725(2*n, n) ;
end proc:
seq(A026726(n), n=0..10) ; # R. J. Mathar, Oct 26 2019

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