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A104625 Expansion of 1/(sqrt(1-4*x) - x^2). 2
1, 2, 7, 24, 87, 322, 1211, 4604, 17645, 68042, 263655, 1025632, 4002601, 15662422, 61427543, 241386924, 950160607, 3745589510, 14784496003, 58424093536, 231112008371, 915065382154, 3626113490579, 14379912928572, 57064644495359 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Diagonal sums of convolution triangle of central binomial coefficients A054335.

Number of lattice paths from (0,0) to (n,n) with steps (0,1), (1,0) and, when on the diagonal, (2,2). - Alois P. Heinz, Sep 14 2016

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

Conjecture: n*a(n) + (n-3)*a(n-1) + 2*(-28*n+51)*a(n-2) + 72*(2*n-5)*a(n-3) - n*a(n-4) + (-5*n+3)*a(n-5) + 18*(2*n-5)*a(n-6) = 0. - R. J. Mathar, Feb 20 2015

MATHEMATICA

CoefficientList[Series[1/(Sqrt[1-4*x] -x^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 12 2018 *)

PROG

(PARI) x='x+O('x^50); Vec(1/(sqrt(1-4*x) - x^2)) \\ G. C. Greubel, Aug 12 2018

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!(1/(sqrt(1-4*x) - x^2))); // G. C. Greubel, Aug 12 2018

CROSSREFS

Cf. A000984, A026671, A054335.

Sequence in context: A183876 A227824 A270490 * A221454 A151293 A122446

Adjacent sequences:  A104622 A104623 A104624 * A104626 A104627 A104628

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 17 2005

STATUS

approved

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Last modified November 20 09:16 EST 2018. Contains 317385 sequences. (Running on oeis4.)