A239168 - OEIS

A239168

Number of partitions of 9^n into parts that are at most n with at least one part of each size.

%I #9 Jul 19 2017 15:47:41

%S 0,1,40,43923,1956835062,4219267293723828,490589938553810921101750,

%T 3299246284983094033572923631218500,

%U 1347808520417651710823757078029174789058075682,34687813181057391872792859998288408847592250236051615502024

%N Number of partitions of 9^n into parts that are at most n with at least one part of each size.

%H Alois P. Heinz, <a href="/A239168/b239168.txt">Table of n, a(n) for n = 0..34</a>

%H A. V. Sills and D. Zeilberger, <a href="https://arxiv.org/abs/1108.4391">Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)</a> (arXiv:1108.4391 [math.CO])

%F a(n) = [x^(9^n-n*(n+1)/2)] Product_{j=1..n} 1/(1-x^j).

%F a(n) ~ 9^(n*(n-1)) / (n!*(n-1)!). - _Vaclav Kotesovec_, Jun 05 2015

%Y Column k=9 of A238012.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Mar 11 2014