A258672 - OEIS

A258672

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

%I #7 Nov 05 2025 15:22:29

%S 0,1,5,61,2280,273052,110537709,156456474138,790541795804221,

%T 14445283925963101577,963056085414756870071490,

%U 235864774408401842540220265704,213426797830699546133563821747980513,717147073290996884137625501875655000693923

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

%C 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.

%H Vaclav Kotesovec, <a href="/A258672/b258672.txt">Table of n, a(n) for n = 0..59</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) ~ n^n * 2^(n*(n-1)) / (n!)^2.

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

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jun 07 2015