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A126932 Binomial transform of A127358. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 15 01:56 EDT 2020. Contains 336485 sequences. (Running on oeis4.)