OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
FORMULA
From Philippe Deléham, Feb 11 2009: (Start)
From Philippe Deléham, Feb 02 2014: (Start)
a(n) = Sum_{k=0..n} A236843(n+k,2*k).
a(n) = Sum_{k=0..n} A236830(n,k).
a(n) = A236830(n+1,1).
a(n) = A165407(3*n).
G.f.: C(x)/(1-x*C(x)^3), C(x) the g.f. of A000108. (End)
n*(5*n-11)*a(n) +2*(-20*n^2+59*n-30)*a(n-1) +15*(5*n^2-19*n+16)*a(n-2) +2*(5*n-6)*(2*n-5)*a(n-3)=0. - R. J. Mathar, Oct 26 2019
n*a(n) +(-7*n+4)*a(n-1) +(7*n-2)*a(n-2) +(19*n-60)*a(n-3) +2*(2*n-7)*a(n-4)=0. - R. J. Mathar, Oct 26 2019
MAPLE
A026726 := proc(n)
A026725(2*n, n) ;
end proc:
seq(A026726(n), n=0..10) ; # R. J. Mathar, Oct 26 2019
MATHEMATICA
CoefficientList[Series[4*x*(1-Sqrt[1-4*x])/(8*x^2-(1-Sqrt[1-4*x])^3), {x, 0, 30}], x] (* G. C. Greubel, Jul 16 2019 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(4*x*(1-sqrt(1-4*x))/(8*x^2-(1-sqrt(1-4*x))^3)) \\ G. C. Greubel, Jul 16 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 4*x*(1-Sqrt(1-4*x))/(8*x^2-(1-Sqrt(1-4*x))^3) )); // G. C. Greubel, Jul 16 2019
(Sage) (4*x*(1-sqrt(1-4*x))/(8*x^2-(1-sqrt(1-4*x))^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jul 16 2019
(GAP) List([0..30], n-> Sum([0..n], k-> (2*k+1)*Binomial(2*n, n-k)*
Fibonacci(k+1)/(n+k+1) )); # G. C. Greubel, Jul 16 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved