|
%I #22 Sep 08 2022 08:44:49
%S 1,6,28,121,508,2109,8723,36065,149277,618961,2571503,10704390,
%T 44641793,186492242,780275596,3269135406,13713525610,57588530626,
%U 242068874444,1018378855512,4287501276956,18062827159136,76141329903018
%N a(n) = T(2n,n+2), T given by A026736.
%H G. C. Greubel, <a href="/A026851/b026851.txt">Table of n, a(n) for n = 2..1000</a>
%F G.f.: (x * C(x)^5)/(1 - x/sqrt(1 - 4 * x)) where C(x) is the g.f. for Catalan numbers A000108. - _David Callan_, Jan 16 2016
%F a(n) ~ (3 - sqrt(5))^5 * (2 + sqrt(5))^(n+2) / (32*sqrt(5)). - _Vaclav Kotesovec_, Jul 18 2019
%t CoefficientList[Series[(1-Sqrt[1-4x])^5/(32 x^5 (1-x/Sqrt[1-4x])), {x, 0, 30}], x] (* _David Callan_, Jan 16 2016 *)
%o (PARI) my(x='x+O('x^30)); Vec(sqrt(1-4*x)*(1-sqrt(1-4*x))^5/(32*x^3*(sqrt(1-4*x) -x)) ) \\ _G. C. Greubel_, Jul 17 2019
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( Sqrt(1-4*x)*(1-Sqrt(1-4*x))^5/(32*x^3*(Sqrt(1-4*x) -x)) )); // _G. C. Greubel_, Jul 17 2019
%o (Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^5/(32*x^3*(sqrt(1-4*x)-x))).series(x, 30).coefficients(x, sparse=False); a[2:] # _G. C. Greubel_, Jul 17 2019
%Y Cf. A000108, A026736.
%K nonn
%O 2,2
%A _Clark Kimberling_
|
