A239167 Number of partitions of 8^n into parts that are at most n with at least one part of each size.

0, 1, 31, 21590, 475473009, 399953578562811, 14325140434481169064975, 23442235543128214521886383970201, 1841132100297745277187328924904656111127054, 7197719612276659958196058354497691622150052900765626132

Offset: 0

Author

Alois P. Heinz, Mar 11 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..35
• 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=8 of A238012.

Formula

a(n) = [x^(8^n-n*(n+1)/2)] Product_{j=1..n} 1/(1-x^j).

a(n) ~ 8^(n*(n-1)) / (n!*(n-1)!). - Vaclav Kotesovec, Jun 05 2015