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%I #15 Sep 08 2022 08:45:29
%S 1,-5,20,-85,350,-1470,6090,-25485,105830,-442150,1838240,-7673330,
%T 31923220,-133186760,554325750,-2311919325,9624918150,-40133290350,
%U 167114005800,-696706389750,2901470571300,-12094930814100,50375156502900,-209972720898450,874600454065500
%N Expansion of 1/(1+5*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
%C Hankel transform is (-5)^n.
%H G. C. Greubel, <a href="/A126987/b126987.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..n} A039599(n,k)*(-6)^k.
%F G.f.: 2/(7 - 5*sqrt(1-4*x)). - _G. C. Greubel_, May 29 2019
%p c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+5*x*c),x=0,27): seq(coeff(ser,x,n),n=0..24); # _Emeric Deutsch_, Mar 23 2007
%t CoefficientList[Series[2/(7-5*Sqrt[1-4*x]), {x,0,30}], x] (* _G. C. Greubel_, May 29 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec(2/(7-5*sqrt(1-4*x))) \\ _G. C. Greubel_, May 29 2019
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(7 - 5*Sqrt(1-4*x)) )); // _G. C. Greubel_, May 29 2019
%o (Sage) (2/(7-5*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 29 2019
%Y Cf. A000108, A039599.
%K sign
%O 0,2
%A _Philippe Deléham_, Mar 21 2007
%E More terms from _Emeric Deutsch_, Mar 23 2007
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