# How does partition function $p(n)/n!$ grow (big-O, etc)?

Specifically, I am interested only in partitions with at least the amount of $2$ in each bucket, but intuitively it doesn't matter?

I have no idea how to work with those complex asymptotic growth formulas. Looking for a simple approximation such as: looks exponential, or looks logarithmic.

• How precise do you need this? It decays faster than $e^{ -n}$. – quid Oct 7 '16 at 0:01
• @quid, the sequence I need an approximation or bound of is: $1, 1, 1, 1, 2, 4, 4, 6, 6, \dots$ are you saying that it eventually decays? – Shine On You Crazy Diamond Oct 7 '16 at 0:06
• @quid, it's to count these babies: math.stackexchange.com/questions/1957311/… – Shine On You Crazy Diamond Oct 7 '16 at 0:07
• I have no idea what your sequence should be. Anyway $3$ has $3$ partitions, namely $1+1+1$, $1+2$, $3$ while $3!=6$. So the third term of the sequence in OP is $1/2$. – quid Oct 7 '16 at 0:09
• @ quid, no 1: {3}, because there must be at least 2 in each bucket. – Shine On You Crazy Diamond Oct 7 '16 at 0:10