A189832 Expansion of 2/((x+3)*sqrt(-3*x^2-2*x+1)+3*x^2+2*x-1).

1, 0, 2, 4, 11, 30, 83, 232, 655, 1860, 5312, 15236, 43863, 126672, 366802, 1064624, 3096347, 9021696, 26328470, 76946524, 225172981, 659711646, 1934891191, 5680457960, 16691655761, 49087826580, 144470474228, 425491536172, 1253971031195, 3697850012310

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=1..(n+1)} (Sum_{j=k..(n+1)} binomial(-k+2*j-1,j-1)*(-1)^(n+1-j)*binomial(n+1,j)))*(1-(-1)^k)/2*(-1)^((k-1)/2)).

D-finite with recurrence: 6*n*a(n) +2*(-2*n+1)*a(n-1) +(-29*n+30)*a(n-2) +(-33*n+47)*a(n-3) +(-17*n+32)*a(n-4) +3*(-n+3)*a(n-5)=0. - R. J. Mathar, Jan 25 2020

Mathematica

CoefficientList[Series[2/((x+3)Sqrt[-3 x^2-2x+1]+3x^2+2x-1), {x, 0, 40}], x] (* Harvey P. Dale, Aug 10 2013 *)

Prog

(Maxima) a(n):=sum((sum(binomial(-k+2*j-1, j-1)*(-1)^(n+1-j)* binomial(n+1, j), j, k, n+1))*(1-(-1)^k)/2*(-1)^((k-1)/2), k, 1, n+1);
(PARI) x='x+O('x^30); Vec(2/((x+3)*sqrt(-3*x^2-2*x+1)+3*x^2+2*x-1)) \\ G. C. Greubel, Jan 14 2018
(Magma) /* Expansion */ Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 30); R!(2/((x+3)*Sqrt(-3*x^2-2*x+1)+3*x^2+2*x-1)); // G. C. Greubel, Jan 14 2018

Crossrefs

Sequence in context: A219017 A285216 A212422 * A193062 A193061 A193060

Adjacent sequences: A189829 A189830 A189831 * A189833 A189834 A189835

Keyword

nonn

Author

Vladimir Kruchinin, May 03 2011

Extensions

More terms from Harvey P. Dale, Aug 10 2013

Status

approved