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A127016 Expansion of 1/(1+7*x*c(x)), c(x) the g.f. of Catalan numbers A000108. 7

%I

%S 1,-7,42,-259,1582,-9702,59388,-363867,2228310,-13649650,83599852,

%T -512063790,3136339276,-19210260076,117662192928,-720683271819,

%U 4414176556902,-27036862348986,165600668448348,-1014304512179994,6212613590747172,-38052263986931796

%N Expansion of 1/(1+7*x*c(x)), c(x) the g.f. of Catalan numbers A000108.

%C Hankel transform is (-7)^n.

%H G. C. Greubel, <a href="/A127016/b127016.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Sum_{k=0..n} A039599(n,k)*(-8)^k.

%F G.f.: 2/(9 - 7*sqrt(1-4*x)). - _G. C. Greubel_, May 31 2019

%p c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+7*x*c),x=0,25): seq(coeff(ser,x,n),n=0..22); - _Emeric Deutsch_, Mar 27 2007

%t CoefficientList[Series[2/(9-7*Sqrt[1-4*x]), {x,0,30}], x] (* _G. C. Greubel_, May 31 2019 *)

%o (PARI) my(x='x+O('x^30)); Vec(2/(9-7*sqrt(1-4*x))) \\ _G. C. Greubel_, May 31 2019

%o (MAGMA) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(9 - 7*Sqrt(1-4*x)) )); // _G. C. Greubel_, May 31 2019

%o (Sage) (2/(9-7*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 31 2019

%K sign

%O 0,2

%A _Philippe Deléham_, Mar 21 2007

%E More terms from _Emeric Deutsch_, Mar 27 2007

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Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)