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

1,1

Links

Table of n, a(n) for n=1..19.

Eric Weisstein's World of Mathematics, Lattice Path

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]

Maple

seq(2*sum(binomial(2*n, k)^2, k=0..(n-1)), n=1..20); # Dennis P. Walsh, Mar 23 2012

Mathematica

Table[Binomial[4n, 2n] - Binomial[2n, n]^2, {n, 1, 20}]

Crossrefs

Cf. A000984, A002894.

Sequence in context: A005261 A104898 A218432 * A273052 A098704 A119298

Adjacent sequences: A071796 A071797 A071798 * A071800 A071801 A071802

Keyword

easy,nice,nonn

Author

T. D. Noe, Jun 06 2002

Status

approved