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A104625 Expansion of 1/(sqrt(1-4*x) - x^2). 3
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
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
a(n) = Sum_{k=0..floor(n+2)/2)} 4^(n+2-2*k) * binomial(n+1-3*k/2,n+2-2*k). - Seiichi Manyama, Feb 06 2024
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
Sequence in context: A183876 A227824 A270490 * A221454 A151293 A122446
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 17 2005
STATUS
approved

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)