A026841 a(n) = T(2n,n-4), T given by A026725.

1, 11, 79, 471, 2535, 12809, 62067, 292085, 1345718, 6102780, 27343148, 121359692, 534632836, 2341151646, 10201950700, 44278673806, 191540714294, 826265471868, 3555992623850, 15273547250820, 65491352071266, 280412963707416

Offset: 4

Author

Clark Kimberling

Keywords

• nonn

Comments

Column k=10 of triangle A236830. - Philippe Deléham, Feb 02 2014

Links

• G. C. Greubel, Table of n, a(n) for n = 4..1000

Crossrefs

Cf. A236830.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-4*x))^10/(128*x^4*(8*x^2 -(1-Sqrt(1-4*x))^3 )) )); // G. C. Greubel, Jul 17 2019

Mathematica

Drop[CoefficientList[Series[(1-Sqrt[1-4*x])^10/(128*x^4*(8*x^2 -(1 - Sqrt[1-4*x])^3 )), {x,0,40}], x], 4] (* G. C. Greubel, Jul 17 2019 *)

PARI

my(x='x+O('x^40)); Vec((1-sqrt(1-4*x))^10/(128*x^4*(8*x^2 -(1 - sqrt(1-4*x))^3 ))) \\ G. C. Greubel, Jul 17 2019

Sage

a=((1-sqrt(1-4*x))^10/(128*x^4*(8*x^2 -(1-sqrt(1-4*x))^3 ))).series(x, 45).coefficients(x, sparse=False); a[4:40] # G. C. Greubel, Jul 17 2019

Formula

a(n) = A026848(n). - Philippe Deléham, Feb 02 2014

G.f.: (x^4*C(x)^10)/(1-x*C(x)^3) where C(x) is the g.f. of A000108. - Philippe Deléham, Feb 02 2014

D-finite with recurrence (n+4)*(3421*n+2687)*a(n) +(3421*n^2-245139*n-819238)*a(n-1) +3*(-126201*n^2+820641*n+1451992)*a(n-2) +(1944367*n^2-12105285*n+5094446)*a(n-3) +6*(-438489*n^2+3204217*n-6453730)*a(n-4) -12*(2*n-7)*(30601*n-111490)*a(n-5)=0. - R. J. Mathar, Jul 22 2025