A026855 a(n) = T(2n+1,n+2), T given by A026736.

1, 5, 21, 85, 342, 1380, 5598, 22836, 93640, 385734, 1595232, 6619374, 27545269, 114901685, 480282369, 2011058681, 8433331523, 35410037683, 148842787215, 626234799703, 2636930617597, 11111302351505, 46848507630321, 197631791675365

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..1580

Formula

G.f.: (x*C(x)^4)/(1 - x/sqrt(1 - 4*x)) where C(x) is the g.f. for Catalan numbers A000108. - David Callan, Jan 16 2016

a(n) ~ (3 - sqrt(5))^4 * (2 + sqrt(5))^(n+2) / (16*sqrt(5)). - Vaclav Kotesovec, Jul 18 2019

D-finite with recurrence -2*(n+3)*(26*n-53)*a(n) +(627*n^2-491*n-2440)*a(n-1) +2*(-1234*n^2+3198*n+337)*a(n-2) +(2957*n^2-13637*n+15888)*a(n-3) +2*(211*n-368)*(2*n-5)*a(n-4)=0. - R. J. Mathar, Nov 22 2024

Maple

gf := ((-2*x^3+12*x^2-7*x+1)*sqrt(1-4*x)+16*x^3-24*x^2+9*x-1)/(2*(x^2+4*x-1)*x^3):
S:= series(gf, x, 40):
seq(coeff(S, x, j), j=1..30); # Robert Israel, Jan 17 2016

Mathematica

CoefficientList[Series[(1-Sqrt[1-4x])^4/(16*x^4*(1-x/Sqrt[1-4x])), {x, 0, 30}], x] (* David Callan, Jan 16 2016 *)

Prog

(PARI) my(x='x+O('x^30)); Vec( sqrt(1-4*x)*(1-sqrt(1-4*x))^4/(16*x^3*(sqrt(1-4*x) -x)) ) \\ G. C. Greubel, Jul 17 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( Sqrt(1-4*x)*(1-Sqrt(1-4*x))^4/(16*x^3*(Sqrt(1-4*x) -x)) )); // G. C. Greubel, Jul 17 2019
(Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^4/(16*x^3*(sqrt(1-4*x) -x))).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Jul 17 2019

Crossrefs

Cf. A000108, A026736.

Sequence in context: A084241 A002450 A187063 * A272832 A273489 A097113

Adjacent sequences: A026852 A026853 A026854 * A026856 A026857 A026858

Keyword

nonn

Author

Clark Kimberling

Status

approved