A026672 a(n) = T(2n,n-1), T given by A026670. Also T(2n,n-1)=T(2n+1,n+2), T given by A026725; and T(2n,n-1), T given by A026736.

1, 5, 22, 94, 398, 1680, 7085, 29877, 126021, 531751, 2244627, 9478605, 40040183, 169193597, 715143046, 3023492646, 12785541850, 54076955716, 228759017624, 967850695362, 4095387893312, 17331318506030

Offset

2,2

Comments

Column k=4 of triangle A236830. - Philippe Deléham, Feb 02 2014

Links

G. C. Greubel, Table of n, a(n) for n = 2..1000

Formula

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

Conjecture: -(n+1)*(n-6)*a(n) +2*(4*n^2-23*n+3)*a(n-1) +3*(-5*n^2+33*n-42)*a(n-2) -2*(2*n-3)*(n-5)*a(n-3)=0. - R. J. Mathar, Aug 08 2015

Mathematica

Drop[CoefficientList[Series[(1-Sqrt[1-4*x])^4/(2*(8*x^2 -(1-Sqrt[1-4*x] )^3)), {x, 0, 30}], x], 2] (* G. C. Greubel, Jul 16 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec( (1-sqrt(1-4*x))^4/(2*(8*x^2 -(1-sqrt(1-4*x))^3))) \\ G. C. Greubel, Jul 16 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(  (1-Sqrt(1-4*x))^4/(2*(8*x^2 -(1-Sqrt(1-4*x))^3)) )); // G. C. Greubel, Jul 16 2019
(Sage) a=((1-sqrt(1-4*x))^4/(2*(8*x^2 -(1-sqrt(1-4*x))^3))).series(x, 30).coefficients(x, sparse=False); a[2:] # G. C. Greubel, Jul 16 2019

Crossrefs

Cf. A000108, A026670, A026725, A026736, A236830.

Sequence in context: A095932 A000346 A289798 * A049652 A026877 A128746

Adjacent sequences: A026669 A026670 A026671 * A026673 A026674 A026675

Keyword

nonn

Author

Clark Kimberling

Status

approved