A071799 Number of lattice paths in the lattice [0..2n] X [0..2n] which do not pass through the point (n,n).
2, 34, 524, 7970, 121252, 1850380, 28337976, 435443490, 6711230900, 103711749284, 1606464657096, 24935144010764, 387746052588104, 6039349005200440, 94203136553911024, 1471326505700038434, 23007323485217888340, 360154459563530689204, 5643332975601670914600
Offset: 1
Links
- Eric Weisstein's World of Mathematics, Lattice Path
Programs
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Maple
seq(2*sum(binomial(2*n,k)^2,k=0..(n-1)),n=1..20); # Dennis P. Walsh, Mar 23 2012
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Mathematica
Table[Binomial[4n, 2n] - Binomial[2n, n]^2, {n, 1, 20}]
Formula
a(n) = binomial(4n, 2n) - binomial(2n, n)^2.
Also, a(n) = 2*Sum_{k=0..n-1} binomial(2n,k)^2. [Dennis P. Walsh, Mar 23 2012]