Changes

<math>

<math>

   \begin{align}

   \begin{align}

\binom{P+A-1}{A-1}     &, A < P \\

F(P,A) &=  \sum_{i=1}^{P} \| \{\text{i distinct alleles observed in a set of P alleles}\} \| \\

\sum_{i=1}^{P-1} \binom{A}{i}\binom{P-1}{i-1}  + \binom{A}{P} &, A \ge P

          &=  \sum_{i=1}^{P-1} \| \{\text{i distinct alleles observed in a set of P alleles}\} \|  + \| \{\text{P distinct alleles observed in a set of P alleles}\} \| \\

          &=  \sum_{i=1}^{P-1} \| \{\text{no ways to choose i distinct alleles}\} \|\| \{\text{no ways to arrange i distinct alleles in a set of P alleles}\} \|  + \| \{\text{P distinct alleles observed in a set of P alleles}\} \| \\

&=  \sum_{i=1}^{P-1} \binom{A}{i}\binom{P-1}{i-1}  + \binom{A}{P}  

   \end{align}

   \end{align}

</math>

</math>

where P is the ploidy number and A is the number of alleles.

= Derivation for indexing the number of genotypes =