A258672 Number of partitions of n*2^n into parts that are at most n.

0, 1, 5, 61, 2280, 273052, 110537709, 156456474138, 790541795804221, 14445283925963101577, 963056085414756870071490, 235864774408401842540220265704, 213426797830699546133563821747980513, 717147073290996884137625501875655000693923

Offset: 0

Author

Vaclav Kotesovec, Jun 07 2015

Keywords

• nonn

Comments

Conjecture: If f(n) >= O(n^4) then "number of partitions of f(n) into parts that are at most n" is asymptotic to f(n)^(n-1) / (n!*(n-1)!). For the examples see A238016 and A238010.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..59
• 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

Cf. A236810, A237998, A238000, A238010, A238016.

Formula

a(n) ~ n^n * 2^(n*(n-1)) / (n!)^2.