A238615 Number of partitions of n^10 into parts that are at most n.

1, 1, 513, 290594892, 8006513870533064, 3157977415776418319210477, 9355115500676554620340590943203672, 139997247522791157386395916200494707946968395, 8097446373533819684208223226876398545717123633973546819

Offset: 0

Author

Alois P. Heinz, Mar 01 2014

Keywords

• nonn

Comments

In general, for m > 3, is "Number of partitions of n^m into parts that are at most n" asymptotic to exp(2*n) * n^((m-2)*n-m) / (2*Pi). - Vaclav Kotesovec, May 25 2015

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..60

Crossrefs

Column k=10 of A238016.

Formula

a(n) = [x^(n^10)] Product_{j=1..n} 1/(1-x^j).

a(n) ~ exp(2*n) * n^(8*n-10) / (2*Pi). - Vaclav Kotesovec, May 25 2015