A126932 Binomial transform of A127358.

1, 4, 15, 55, 199, 714, 2547, 9048, 32043, 113212, 399265, 1406079, 4946137, 17383162, 61048359, 214270215, 751691811, 2636004228, 9240836733, 32386215981, 113478349989, 397544907486, 1392493797765, 4876916883090, 17078574481941, 59802541979964

Offset

0,2

Comments

Hankel transform is (-1)^n.

Row sums of the Riordan array ((1-2*x)/(1+x+x^2), x/(1+x+x^2))^(-1). - Paul Barry, Nov 06 2008

Links

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

Isaac DeJager, Madeleine Naquin, Frank Seidl, Colored Motzkin Paths of Higher Order, VERUM 2019.

Formula

a(n+1) = 3*a(n) + A059738(n) with a(0)=1.

G.f: (sqrt(1-2*x-3*x^2) + 3*(1-3*x))/(2*(2-13*x+21*x^2)). - Paul Barry, Nov 06 2008

Conjecture: +2*n*a(n) -11*n*a(n-1) +4*(2*n+3)*a(n-2) +21*(n-2)*a(n-3)=0. - R. J. Mathar, Nov 24 2012

a(n) ~ 3 * 7^n / 2^(n+1). - Vaclav Kotesovec, Feb 12 2014

Maple

seq(coeff(series( (sqrt(1-2*x-3*x^2) + 3*(1-3*x))/(2*(2-13*x+21*x^2)), x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 29 2020

Mathematica

CoefficientList[Series[(Sqrt[-3*x^2-2*x+1]-3*(3*x-1))/(2*(21*x^2-13*x+2)), {x, 0, 30}], x] (* Vaclav Kotesovec, Feb 12 2014 *)

Prog

(PARI) my(x='x+O('x^30)); Vec( (sqrt(1-2*x-3*x^2) + 3*(1-3*x))/(2*(2-13*x+21*x^2)) ) \\ G. C. Greubel, Jan 29 2020
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (Sqrt(1-2*x-3*x^2) + 3*(1-3*x))/(2*(2-13*x+21*x^2)) )); // G. C. Greubel, Jan 29 2020
(Sage)
def A126932_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (sqrt(1-2*x-3*x^2) + 3*(1-3*x))/(2*(2-13*x+21*x^2)) ).list()
A126932_list(30) # G. C. Greubel, Jan 29 2020

Crossrefs

Sequence in context: A219603 A268164 A291029 * A094833 A039717 A220948

Adjacent sequences: A126929 A126930 A126931 * A126933 A126934 A126935

Keyword

nonn

Author

Philippe Deléham, Mar 17 2007

Extensions

Corrected and extended by Vincenzo Librandi, Feb 13 2014

Status

approved