|
%I #18 Sep 08 2022 08:45:29
%S 1,-8,56,-400,2840,-20208,143664,-1021728,7265240,-51665200,367392656,
%T -2612584928,18578329456,-132112749920,939467783520,-6680662171200,
%U 47506922377560,-337827035002800,2402325467002320,-17083203745473120,121480558396908240,-863861754435010080
%N Expansion of 1/(1+8*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
%C Hankel transform is (-8)^n.
%C Catalan transform of (-1)^n*A001018(n). - _R. J. Mathar_, Nov 11 2008
%H G. C. Greubel, <a href="/A126985/b126985.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..n} A039599(n,k)*(-9)^k.
%F G.f.: 2/(10 - 8*sqrt(1-4*x)). - _G. C. Greubel_, May 28 2019
%p c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+8*x*c),x=0,25): seq(coeff(ser,x,n),n=0..21); # _Emeric Deutsch_, Mar 24 2007
%t CoefficientList[Series[2/(10-8*Sqrt[1-4*x]), {x,0,30}], x] (* _G. C. Greubel_, May 28 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec(2/(10-8*sqrt(1-4*x))) \\ _G. C. Greubel_, May 28 2019
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(10-8*Sqrt(1-4*x)) )); // _G. C. Greubel_, May 28 2019
%o (Sage) (2/(10-8*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 28 2019
%Y Cf. A000108, A001018, A039599.
%K sign
%O 0,2
%A _Philippe Deléham_, Mar 21 2007
%E More terms from _Emeric Deutsch_, Mar 24 2007
|
