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%I #14 Sep 08 2022 08:45:29
%S 1,-6,30,-156,798,-4116,21132,-108792,559134,-2876772,14790660,
%T -76080648,391221516,-2012174664,10347690072,-53218984176,
%U 273689323038,-1407575396484,7238848057812,-37228770844776,191460735261828,-984660836306904,5063949044206632,-26043244926688656
%N Expansion of 1/(1+6*x*c(x)), where c(x) = g.f. for Catalan numbers A000108.
%C Hankel transform is (-6)^n.
%H G. C. Greubel, <a href="/A127017/b127017.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..n} A039599(n,k)*(-7)^k.
%F G.f.: 1/(4 - 3*sqrt(1-4*x)). - _G. C. Greubel_, May 31 2019
%p c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+6*x*c),x=0,27): seq(coeff(ser,x,n),n=0..23); # _Emeric Deutsch_, Mar 23 2007
%t CoefficientList[Series[1/(4-3*Sqrt[1-4*x]), {x,0,30}], x] (* _G. C. Greubel_, May 31 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec(1/(4-3*sqrt(1-4*x))) \\ _G. C. Greubel_, May 31 2019
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/(4 - 3*Sqrt(1-4*x)) )); // _G. C. Greubel_, May 31 2019
%o (Sage) (1/(4-3*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 31 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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