Formula:8798

Digital Library of Mathematical Functions ID 27.14.E6

${\displaystyle{\displaystyle p\left(n\right)=\sum_{k=1}^{\infty}(-1)^{k+1}\left(p\left(n-\omega(k)\right)+p\left(n-\omega(-k)\right)\right)=p\left(n-1\right)+p\left(n-2\right)-p\left(n-5\right)-p\left(n-7\right)+\cdots,}}$

Symbols List

• ${\displaystyle{\displaystyle p\left(\NVar{n}\right)}}$: total number of partitions of n
• ${\displaystyle{\displaystyle k}}$: positive integer
• ${\displaystyle{\displaystyle n}}$: positive integer
• ${\displaystyle{\displaystyle\omega(k)}}$: pentagonal numbers (locally)
 

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