A239168 Number of partitions of 9^n into parts that are at most n with at least one part of each size.

0, 1, 40, 43923, 1956835062, 4219267293723828, 490589938553810921101750, 3299246284983094033572923631218500, 1347808520417651710823757078029174789058075682, 34687813181057391872792859998288408847592250236051615502024

Offset: 0

Author

Alois P. Heinz, Mar 11 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..34
• A. V. Sills and D. Zeilberger, Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz) (arXiv:1108.4391 [math.CO])

Crossrefs

Column k=9 of A238012.

Formula

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

a(n) ~ 9^(n*(n-1)) / (n!*(n-1)!). - Vaclav Kotesovec, Jun 05 2015