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%I #19 Aug 12 2017 09:16:00
%S 2,34,524,7970,121252,1850380,28337976,435443490,6711230900,
%T 103711749284,1606464657096,24935144010764,387746052588104,
%U 6039349005200440,94203136553911024,1471326505700038434,23007323485217888340,360154459563530689204,5643332975601670914600
%N Number of lattice paths in the lattice [0..2n] X [0..2n] which do not pass through the point (n,n).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LatticePath.html">Lattice Path</a>
%F a(n) = binomial(4n, 2n) - binomial(2n, n)^2.
%F Also, a(n) = 2*Sum_{k=0..n-1} binomial(2n,k)^2. [_Dennis P. Walsh_, Mar 23 2012]
%p seq(2*sum(binomial(2*n,k)^2,k=0..(n-1)),n=1..20); # _Dennis P. Walsh_, Mar 23 2012
%t Table[Binomial[4n, 2n] - Binomial[2n, n]^2, {n, 1, 20}]
%Y Cf. A000984, A002894.
%K easy,nice,nonn
%O 1,1
%A _T. D. Noe_, Jun 06 2002
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