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4862

4862 is a natural number that sits between 4861 and 4863. It is even and composite, with a prime factorization of 2 × 11 × 13 × 17.

In mathematics, 4862 is best known as the ninth Catalan number, denoted C9. Catalan numbers form a

As a small composite, 4862 has several divisors beyond 1 and itself, including 2, 11, 13, and

In summary, 4862 is notable primarily for its role in combinatorics as the ninth Catalan number and

wide-ranging
sequence
with
many
combinatorial
interpretations.
C9
equals
(1/10)
times
the
binomial
coefficient
binomial(18,
9),
which
evaluates
to
4862.
This
number
counts
various
structures,
including
the
number
of
correctly
matched
sequences
of
nine
pairs
of
parentheses,
Dyck
words
of
semilength
9,
and
monotone
lattice
paths
from
(0,0)
to
(9,9)
that
never
go
above
the
main
diagonal.
They
also
enumerate
full
binary
trees
with
ten
leaves.
17,
as
well
as
their
products
such
as
22,
26,
34,
143,
187,
221,
and
286,
among
others.
for
its
straightforward
prime
factorization.
It
serves
as
an
example
of
how
a
single
integer
can
have
both
a
simple
arithmetic
structure
and
a
rich
combinatorial
interpretation.
See
also
Catalan
numbers,
binomial
coefficients,
and
Dyck
paths
for
related
topics.