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A026672 a(n) = T(2n,n-1), T given by A026670. Also T(2n,n-1)=T(2n+1,n+2), T given by A026725; and T(2n,n-1), T given by A026736.

%I A026672 #15 Sep 08 2022 08:44:49
%S A026672 1,5,22,94,398,1680,7085,29877,126021,531751,2244627,9478605,40040183,
%T A026672 169193597,715143046,3023492646,12785541850,54076955716,228759017624,
%U A026672 967850695362,4095387893312,17331318506030
%N A026672 a(n) = T(2n,n-1), T given by A026670. Also T(2n,n-1)=T(2n+1,n+2), T given by A026725; and T(2n,n-1), T given by A026736.
%C A026672 Column k=4 of triangle A236830. - _Philippe Deléham_, Feb 02 2014
%H A026672 G. C. Greubel, <a href="/A026672/b026672.txt">Table of n, a(n) for n = 2..1000</a>
%F A026672 G.f.: (x*C(x)^4)/(1-x*C(x)^3), where C(x) is the g.f. of A000108. - _Philippe Deléham_, Feb 02 2014
%F A026672 Conjecture: -(n+1)*(n-6)*a(n) +2*(4*n^2-23*n+3)*a(n-1) +3*(-5*n^2+33*n-42)*a(n-2) -2*(2*n-3)*(n-5)*a(n-3)=0. - _R. J. Mathar_, Aug 08 2015
%t A026672 Drop[CoefficientList[Series[(1-Sqrt[1-4*x])^4/(2*(8*x^2 -(1-Sqrt[1-4*x] )^3)), {x,0,30}], x], 2] (* _G. C. Greubel_, Jul 16 2019 *)
%o A026672 (PARI) my(x='x+O('x^30)); Vec( (1-sqrt(1-4*x))^4/(2*(8*x^2 -(1-sqrt(1-4*x))^3))) \\ _G. C. Greubel_, Jul 16 2019
%o A026672 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(  (1-Sqrt(1-4*x))^4/(2*(8*x^2 -(1-Sqrt(1-4*x))^3)) )); // _G. C. Greubel_, Jul 16 2019
%o A026672 (Sage) a=((1-sqrt(1-4*x))^4/(2*(8*x^2 -(1-sqrt(1-4*x))^3))).series(x, 30).coefficients(x, sparse=False); a[2:] # _G. C. Greubel_, Jul 16 2019
%Y A026672 Cf. A000108, A026670, A026725, A026736, A236830.
%K A026672 nonn
%O A026672 2,2
%A A026672 _Clark Kimberling_