###### Av(132)

Generating Function

\(\displaystyle \frac{1-\sqrt{1-4 x}}{2 x}\)

Counting Sequence

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, ...

Implicit Equation for the Generating Function

\(\displaystyle x F \left(x
\right)^{2}-F \! \left(x \right)+1 = 0\)

Recurrence

\(\displaystyle a \! \left(0\right) = 1\)

\(\displaystyle a \! \left(n +1\right) = \frac{2 \left(1+2 n \right) a \! \left(n \right)}{n +2}, \quad n \geq 1\)

\(\displaystyle a \! \left(n +1\right) = \frac{2 \left(1+2 n \right) a \! \left(n \right)}{n +2}, \quad n \geq 1\)

### This specification was found using the strategy pack "Point Placements" and has 5 rules.

Found on May 17, 2021.Finding the specification took 0 seconds.

\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
\end{align*}\)