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%I #28 Sep 04 2017 04:02:24
%S 1,2,7,35,200,1201,7389,46149,291306,1853581,11868586,76380826,
%T 493606726,3201081874,20821158234,135776966762,887393271311,
%U 5811082966886,38119865826421,250447855600321,1647729357535486,10854207824989831,71581930485576631,472560922429972951,3122648143126315651
%N a(n) = (1/3)*(2 + Sum_{k=0..n} C(3k,k)).
%H Vincenzo Librandi, <a href="/A024719/b024719.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = Sum_{k=0..n} C(k-n,2n-2k). - _Paul Barry_, Mar 15 2010
%F G.f.: (1-2*g)/((3*g-1)*(g^3-2*g^2+g-1)) where g*(1-g)^2 = x. - _Mark van Hoeij_, Nov 09 2011
%F Conjecture: 2*n*(2*n-1)*a(n) + (-31*n^2 + 29*n - 6)*a(n-1) +3*(3*n-1)*(3*n-2)*a(n-2) = 0. - _R. J. Mathar_, Sep 29 2012
%F a(n) ~ 3^(3*n + 5/2)/(23*2^(2*n+1)*sqrt(Pi*n)). - _Vaclav Kotesovec_, Oct 07 2012
%t Table[Sum[Binomial[k-n,2n-2k],{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 07 2012 *)
%o (PARI) a(n)=sum(k=0,n, binomial(k-n,2*(n-k)) ); \\ _Joerg Arndt_, May 04 2013
%K nonn
%O 0,2
%A _Clark Kimberling_
%E More terms from _James A. Sellers_, May 01 2000
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