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A026855 a(n) = T(2n+1,n+2), T given by A026736.

%I A026855 #27 Nov 22 2024 07:16:33
%S A026855 1,5,21,85,342,1380,5598,22836,93640,385734,1595232,6619374,27545269,
%T A026855 114901685,480282369,2011058681,8433331523,35410037683,148842787215,
%U A026855 626234799703,2636930617597,11111302351505,46848507630321,197631791675365
%N A026855 a(n) = T(2n+1,n+2), T given by A026736.
%H A026855 Robert Israel, <a href="/A026855/b026855.txt">Table of n, a(n) for n = 1..1580</a>
%F A026855 G.f.: (x*C(x)^4)/(1 - x/sqrt(1 - 4*x)) where C(x) is the g.f. for Catalan numbers A000108. - _David Callan_, Jan 16 2016
%F A026855 a(n) ~ (3 - sqrt(5))^4 * (2 + sqrt(5))^(n+2) / (16*sqrt(5)). - _Vaclav Kotesovec_, Jul 18 2019
%F A026855 D-finite with recurrence -2*(n+3)*(26*n-53)*a(n) +(627*n^2-491*n-2440)*a(n-1) +2*(-1234*n^2+3198*n+337)*a(n-2) +(2957*n^2-13637*n+15888)*a(n-3) +2*(211*n-368)*(2*n-5)*a(n-4)=0. - _R. J. Mathar_, Nov 22 2024
%p A026855 gf := ((-2*x^3+12*x^2-7*x+1)*sqrt(1-4*x)+16*x^3-24*x^2+9*x-1)/(2*(x^2+4*x-1)*x^3):
%p A026855 S:= series(gf,x,40):
%p A026855 seq(coeff(S,x,j),j=1..30); # _Robert Israel_, Jan 17 2016
%t A026855 CoefficientList[Series[(1-Sqrt[1-4x])^4/(16*x^4*(1-x/Sqrt[1-4x])), {x, 0, 30}], x] (* _David Callan_, Jan 16 2016 *)
%o A026855 (PARI) my(x='x+O('x^30)); Vec( sqrt(1-4*x)*(1-sqrt(1-4*x))^4/(16*x^3*(sqrt(1-4*x) -x)) ) \\ _G. C. Greubel_, Jul 17 2019
%o A026855 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( Sqrt(1-4*x)*(1-Sqrt(1-4*x))^4/(16*x^3*(Sqrt(1-4*x) -x)) )); // _G. C. Greubel_, Jul 17 2019
%o A026855 (Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^4/(16*x^3*(sqrt(1-4*x) -x))).series(x, 30).coefficients(x, sparse=False); a[1:] # _G. C. Greubel_, Jul 17 2019
%Y A026855 Cf. A000108, A026736.
%K A026855 nonn
%O A026855 1,2
%A A026855 _Clark Kimberling_