A026842 a(n) = T(2n,n-3), T given by A026725.

1, 9, 56, 300, 1487, 7041, 32381, 146017, 649395, 2859231, 12494914, 54291912, 234860677, 1012433965, 4352210327, 18666918033, 79916230409, 341615895659, 1458457275715, 6220016154525, 26503542364381, 112847001503099, 480173686483581

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Comments

Column k=8 of triangle A236830. - Philippe Deléham, Feb 02 2014

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A236830, A026846, A026849.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-Sqrt(1-4*x))^8/(32*x^3*(8*x^2 -(1-Sqrt(1-4*x))^3 )) )); // G. C. Greubel, Jul 17 2019

Mathematica

Drop[CoefficientList[Series[(1-Sqrt[1-4*x])^8/(32*x^3*(8*x^2 -(1 - Sqrt[1-4*x])^3 )), {x,0,30}], x],3] (* G. C. Greubel, Jul 17 2019 *)

PARI

my(x='x+O('x^30)); Vec((1-sqrt(1-4*x))^8/(32*x^3*(8*x^2 -(1 - sqrt(1-4*x))^3 ))) \\ G. C. Greubel, Jul 17 2019

Sage

a=((1-sqrt(1-4*x))^8/(32*x^3*(8*x^2 -(1-sqrt(1-4*x))^3 ))).series(x, 30).coefficients(x, sparse=False); a[3:] # G. C. Greubel, Jul 17 2019

Formula

a(n) = A026846(n) = A026849(n). - Philippe Deléham, Feb 02 2014

G.f.: (x^3*C(x)^8)/(1-x*C(x)^3) where C(x) is the g.f. of A000108. - Philippe Deléham, Feb 02 2014

D-finite with recurrence -(n+3)*(253*n-940)*a(n) +(3061*n^2-6571*n-18156)*a(n-1) +(-12091*n^2+43849*n-996)*a(n-2) +(14543*n^2-76721*n+109596)*a(n-3) +2*(1037*n-2568)*(2*n-5)*a(n-4)=0. - R. J. Mathar, Jul 22 2025