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
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 17 2005
STATUS
approved