OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Lattice Path
FORMULA
a(n) = binomial(4*n, 2*n) - binomial(2*n, n)^2.
a(n) = 2*Sum_{k=0..n-1} binomial(2*n,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}]
PROG
(Python)
from math import comb
def A071799(n): return comb((m:=n<<1)<<1, m)-comb(m, n)**2 # Chai Wah Wu, Sep 12 2025
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
T. D. Noe, Jun 06 2002
STATUS
approved