A026759 a(n) = T(2n, n), T given by A026758.

1, 2, 7, 27, 109, 453, 1922, 8284, 36155, 159435, 709246, 3178992, 14343567, 65099245, 297015765, 1361584755, 6268757195, 28975155915, 134410918700, 625578384150, 2920488902795, 13672762887465, 64179220019365, 301987822527627

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A026758, A026760, A026761, A026762, A026763, A026764, A026765, A026766, A026767, A026768.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( ((1-x)*Sqrt(1 - 4*x) - Sqrt(1 - 6*x + 5*x^2))/(2*x^2) )); // G. C. Greubel, Oct 31 2019

Maple

seq(coeff(series(((1-x)*sqrt(1-4*x) - sqrt(1 -6*x +5*x^2))/(2*x^2), x, n+2), x, n), n = 0..30); # G. C. Greubel, Oct 31 2019

Mathematica

CoefficientList[Normal[Series[((1-x)Sqrt[1-4x] -Sqrt[1-6x+5x^2])/(2x^2), {x, 0, 30}]], x] (* David Callan, Feb 01 2014 *)

PARI

my(x='x+O('x^30)); Vec(((1-x)*sqrt(1 - 4*x) - sqrt(1 - 6*x + 5*x^2))/(2*x^2)) \\ G. C. Greubel, Oct 31 2019

Sage

def A077952_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(((1-x)*sqrt(1-4*x) - sqrt(1-6*x+5*x^2))/(2*x^2)).list()
A077952_list(30) # G. C. Greubel, Oct 31 2019

Formula

a(n) = A002212(n+1) - A000245(n). - David Callan, Feb 01 2014

G.f.: ((1-x)*sqrt(1 - 4*x) - sqrt(1 - 6*x + 5*x^2))/(2*x^2). - G. C. Greubel, Oct 31 2019