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A071799 Number of lattice paths in the lattice [0..2n] X [0..2n] which do not pass through the point (n,n). 0
2, 34, 524, 7970, 121252, 1850380, 28337976, 435443490, 6711230900, 103711749284, 1606464657096, 24935144010764, 387746052588104, 6039349005200440, 94203136553911024, 1471326505700038434, 23007323485217888340, 360154459563530689204, 5643332975601670914600 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 21 16:47 EDT 2021. Contains 345365 sequences. (Running on oeis4.)