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%I #16 Jun 14 2016 03:18:28
%S 1,0,6,8,54,144,636,2160,8550,31520,121716,462000,1780156,6840288,
%T 26436024,102245472,396589446,1540427328,5994280644,23356702512,
%U 91133123796,355991626848,1392115710024,5449199307552,21349205067996
%N Convolution of the central binomial coefficients A000984(n) and (-2)^n.
%C Hankel transform is A102591.
%H G. C. Greubel, <a href="/A167481/b167481.txt">Table of n, a(n) for n = 0..500</a>
%F G.f.: 1/((1+2x)*sqrt(1-4x)).
%F a(n) = Sum_{k=0..n} (-2)^(n-k)*C(2k,k).
%F Conjecture: n*a(n) + 2*(1-n)*a(n-1) + 4*(1-2n)*a(n-2) = 0. - _R. J. Mathar_, Nov 16 2011
%F a(n) = (-2)^n*JacobiP(n, 1/2, -1-n, -5). - _Peter Luschny_, Aug 02 2014
%t Table[FullSimplify[(-2)^n/Sqrt[3] + 1/2*Binomial[2*(1+n),1+n] * Hypergeometric2F1[1,3/2+n,2+n,-2]],{n,0,20}] (* _Vaclav Kotesovec_, Jan 31 2014 *)
%t CoefficientList[Series[1/((1 + 2*t)*Sqrt[1 - 4 t]), {t,0,50}], t] (* _G. C. Greubel_, Jun 13 2016 *)
%Y Cf. A000984, A102591.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Nov 04 2009
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